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Determine whether each equation is a linear equation. Write yes or no****. If yes, write the equation in
standard form.
x = y ± 5
Rewrite the equation in standard form.
The equation is now in standard form where A = 1, B = ±1, and C = ±5. This is a linear equation.
± 2 x ± 3 = y
Rewrite the equation in standard form.
The equation is now in standard form where A = 2, B = 1, and C = ±3. This is a linear equation.
± 4 y + 6 = 2
Rewrite the equation in standard form.
The equation is now in standard form where A = 0, B = 1, and C = 1. This is a linear equation.
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3 - 1 Graphing Linear Equations
The equation is now in standard form where A = 0, B = 1, and C = 1. This is a linear equation.
Rewrite the equation in standard form.
The equation is now in standard form where A = 2, B = ±1, and C = 6. This is a linear equation.
Find the x - and y
-
intercepts of the graph of each linear function. Describe what the intercepts mean.
The x - intercept is the point at which the y - coordinate is 0, or the line crosses the x - axis. So, the x - intercept is 25.
The y - intercept is the point at which the x - coordinate is 0, or the line crosses the y - axis. So, the y - intercept is ±4.
The x- LQWHUFHSWPHDQVWKDWDIWHUPLQXWHVWKHWHPSHUDWXUHLV)7KH y- intercept ±4 means that at time 0, the
temperature is ±)
The x - intercept is the point at which the y - coordinate is 0, or the line crosses at the x - axis. So, the x - intercept is 12.
The y - intercept is the point at which the x - coordinate is 0, or the line crosses at the y - axis. So, the y - intercept is ±24.
The x - intercept 12 means that after 12 seconds, the scuba diver is at a depth of 0 meters, or at the surface. The y -
intercept ±24 means that at time 0, the scuba diver is at a depth of ±24 meters, or 24 meters below sea level.
Graph each equation by using the x - and y - intercepts.
y = 4 + x
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3 - 1 Graphing Linear Equations
2 x ± 5 y = 1
To find the x - intercept, let y = 0.
To find the y - intercept, let x = 0.
So, the x - intercept is , and the y - intercept is. Plot these two points, and then draw a line through them.
Graph each equation by making a table.
x + 2 y = 4
Solve for y.
Select values from the domain and make a table. Create ordered pairs and graph them.
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3 - 1 Graphing Linear Equations
Graph each equation by making a table.
x + 2 y = 4
Solve for y.
Select values from the domain and make a table. Create ordered pairs and graph them.
x
y ( x, y )
±3 + 2 y = ± 5
Select values from the domain and make a table. Create ordered pairs and graph them.
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3 - 1 Graphing Linear Equations
a. Use the x- and y- intercepts to graph the equation.
b. Describe what these values mean.
a. To find the x - intercept, let y = 0.
To find the y - intercept, let x = 0.
So the x - intercept is 12 and the y - intercept is 6. Plot these points, and then draw a line through them.
b. The x - intercept means that 12 children and 0 adults can attend for $60. The y - intercept means that 0 children and
6 adults can attend for $60.
Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in
standard form.
5 x + y
2
Since y is squared, the equation cannot be written in standard form. So, the equation is not linear.
8 + y = 4 x
Rewrite the equation in standard form.
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3 - 1 Graphing Linear Equations
5 x + y
2
Since y is squared, the equation cannot be written in standard form. So, the equation is not linear.
8 + y = 4 x
Rewrite the equation in standard form.
The equation is now in standard form where A = 4, B = 1, and C = 8.
9 xy ± 6 x = 7
Since there are two variables in one term, the equation cannot be written in standard form. So, the equation is not
linear.
4 y
2
Since y is squared, the equation cannot be written in standard form. So, the equation is not linear.
12 x = 7 y ± 10 y
Rewrite the equation in standard form.
The equation is now in standard form where A = 4, B = 1, and C = 0.
y = 4 x + x
Rewrite the equation in standard form.
The equation is now in standard form where A = 5, B = ±1, and C = 0.
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3 - 1 Graphing Linear Equations
The x - intercept is the point at which the y - coordinate is 0, or the line crosses the x - axis. So, the x - intercept is ±2.
The y - intercept is the point at which the x - coordinate is 0, or the line crosses the y - axis. So, the y - intercept is 2.
Find the x - and y
-
intercepts of each linear function. Describe what the intercepts mean.
The x - intercept is the point at which the y - coordinate is 0, or the line crosses the x - axis. So, the x - intercept is 6.
The y - intercept is the point at which the x - coordinate is 0, or the line crosses the y - axis. So, the y - intercept is 20.
The x - intercept 6 means that the height of the eagle is 0 ft after 6 seconds, or that it takes 6 seconds for the eagle to
land. The y- intercept 20 means that at time 0, the height of the eagle is 20 ft. In other words, the initial height of the
eagle is 20 ft.
The x - intercept is the point at which the y - coordinate is 0, or the line crosses the x - axis. So, the x - intercept is 8.
The y - intercept is the point at which the x - coordinate is 0, or the line crosses the y - axis. So, the y - intercept is 4.
The x - intercept 8 means that after 8 minutes, Eva¶s distance from home is 0 mi., or she is home after 8 minutes. The
y- intercept 4 means that at time 0, Eva¶s distance from home is 4 miles. In other words, she is initially 4 miles from
home.
Graph each equation by using the x ± and y ± intercepts.
y = 4 + 2 x
To find the x - intercept, let y = 0.
To find the y - intercept, let x = 0.
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3 - 1 Graphing Linear Equations
The x - intercept is the point at which the y - coordinate is 0, or the line crosses the x - axis. So, the x - intercept is 8.
The y - intercept is the point at which the x - coordinate is 0, or the line crosses the y - axis. So, the y - intercept is 4.
The x - intercept 8 means that after 8 minutes, Eva¶s distance from home is 0 mi., or she is home after 8 minutes. The
y- intercept 4 means that at time 0, Eva¶s distance from home is 4 miles. In other words, she is initially 4 miles from
home.
Graph each equation by using the x ± and y ± intercepts.
y = 4 + 2 x
To find the x - intercept, let y = 0.
To find the y - intercept, let x = 0.
So, the x - intercept is ±2, and the y - intercept is 4. Plot these two points and then draw a line through them.
5 ± y = ± 3 x
To find the x - intercept, let y = 0.
To find the y - intercept, let x = 0.
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3 - 1 Graphing Linear Equations
x = 5 y + 5
To find the x - intercept, let y = 0.
To find the y - intercept, let x = 0.
So, the x - intercept is 5 and the y - intercept is ±1. Plot these two points and then draw a line through them.
x + y = 4
To find the x - intercept, let y = 0.
To find the y - intercept, let x = 0.
So, the x - intercept is 4 and the y - intercept is 4. Plot these two points and then draw a line through them.
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3 - 1 Graphing Linear Equations
x + y = 4
To find the x - intercept, let y = 0.
To find the y - intercept, let x = 0.
So, the x - intercept is 4 and the y - intercept is 4. Plot these two points and then draw a line through them.
x ± y = ± 3
To find the x - intercept, let y = 0.
To find the y - intercept, let x = 0.
So, the x - intercept is ±3 and the y - intercept is 3. Plot these two points and then draw a line through them.
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3 - 1 Graphing Linear Equations
y = 8 ± 6 x
To find the x - intercept, let y = 0.
To find the y - intercept, let x = 0.
So, the x - intercept is DQGWKH y - intercept is 8. Plot these two points and then draw a line through them.
Graph each equation by making a table.
x = ± 2
Select values from the range and make a table. Create ordered pairs and graph them.
Note that every value in the range is linked to ±2 in the domain.
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3 - 1 Graphing Linear Equations
Graph each equation by making a table.
x = ± 2
Select values from the range and make a table. Create ordered pairs and graph them.
Note that every value in the range is linked to ±2 in the domain.
y = ± 4
Select values from the domain and make a table. Create ordered pairs and graph them.
y = ± 8 x
Select values from the domain and make a table. Create ordered pairs and graph them.
3 x = y
Select values from the domain and make a table. Create ordered pairs and graph them.
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3 - 1 Graphing Linear Equations
x = 10 ± y
Solve x = 10 ± y for\
Select values from the domain and make a table. Create ordered pairs and graph them.
x y = ± x + 10 y ( x, y )
4 y =
2 y =
0 y =
1 y =
2 y =
4 y =
TV RATINGS The number of people who watch a singing competition can be given by p = 0.15 v , where p
represents the number of people in millions who saw the show and v is the number of potential viewers in millions.
a. Make a table of values for the points ( v , p ).
b. Graph the equation.
c. Use the graph to estimate the number of people who saw the show if there are 14 million potential viewers.
d. Explain why it would not make sense for v to be a negative number.
a. Select values from the domain and make a table.
b. Graph the ordered pairs from the table.
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3 - 1 Graphing Linear Equations
TV RATINGS
The number of people who watch a singing competition can be given by p = 0.15 v , where p
represents the number of people in millions who saw the show and v is the number of potential viewers in millions.
a. Make a table of values for the points ( v , p ).
b. Graph the equation.
c. Use the graph to estimate the number of people who saw the show if there are 14 million potential viewers.
d. Explain why it would not make sense for v to be a negative number.
a. Select values from the domain and make a table.
b. Graph the ordered pairs from the table.
c. The table shows that the value of p increases by 0.3 as v increases by 2. So at v = 14, p would be about 2.
million.
d. v < 0 does not make sense because there cannot be fewer than 0 viewers.
Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in
standard form.
x + = 7
Because y is in the denominator of a fraction, the equation cannot be written in standard form. Multiplying each side
by y in order to get y out of the denominator will lead to an xy - term. So, the equation is not linear.
Rewrite the equation in standard form.
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3 - 1 Graphing Linear Equations
