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Intro. To Graphing Linear
Equations
The Coordinate Plane
A. The coordinate plane has 4 quadrants.
B. Each point in the coordinate plain has an x-coordinate ( the abscissa ) and a y-coordinate ( the ordinate ). The point is stated as an ordered pair (x,y).
C. Horizontal Axis is the X – Axis. (y = 0)
D. Vertical Axis is the Y- Axis (x = 0)
Plot the following points:
a) (3,7) b) (-4,5) c) (-6,-1) d) (6,-7)
e) (5,0) f) (0,5) g) (-5,0) f) (0, -5)
y-axis
x-axis
Slope Intercept Form
Before graphing linear equations, we need to be familiar with slope intercept form. To understand slope
intercept form, we need to understand two major terms: The slope and the y-intercept.
Slope (m):
The slope measures the steepness of a non-vertical line. It is sometimes referred to as the rise over run.
It’s how fast and in what direction y changes compared to x.
y-intercept:
The y-intercept is where a line passes through the y axis. It is always stated as an ordered pair (x,y).
The x coordinate is always zero. The y coordinate can be found by plugging in 0 for the X in the equation or by finding exactly where the line crosses the y-axis.
What are the coordinates of the y-intercept line pictured in the diagram above? :
Some of you have worked with slope intercept form of a linear equation before. You may remember:
y = mx + b
Using y = mx + b, can you figure out the equation of the line pictured above?:
3) y = ½ x – 3 4) y= - ⅔x + 2
5) y = -x – 3 6) y= 5x
Q3 Quiz 3 Review
1) y = 4x - 6
2) y = -2x + 7
- y = -x -
- y = 5x +
- y = - ½ x -
- y = ⅗x -
7) y = ⅔x
8) y = - ⅓x + 4
Find the equation in slope intercept form of the line formed by the given points. When you’re finished, graph the equation on the give graph.
- (4,-6) and (-8, 3)
- (4,-3) and (9,-3) 3) (7,-2) and (7, 4)
III. Special Slopes A. Zero Slope B. No Slope (undefined slope)
- No change in Y * No change in X
- Equation will be Y = * Equation will be X =
- Horizontal Line * Vertical Line
m = -2; (-3,1) a) Point-Slope Form b) Slope intercept form c) Standard Form
m = - ¾ ; (-8, 5) Point-Slope Form b) Slope intercept form c) Standard Form
m = ⅔; (-6, -4) Point-Slope Form b) Slope intercept form c) Standard Form
m = -1 (5, -1) Point-Slope Form b) Slope intercept form c) Standard Form
Find equation in slope intercept form and graph:
- (3,-2)(-6,-8) 2) (-6,10) (9,-10)
m = 0 (4,3) 10) m = undefined (-6, 5)
16x -4y =36 12) 8x+24y = 96
y+7=2(x+1) 14) y+5=(2/5)(x+10)
y-7= ¾ (x-12) 16) y-2=-3(x-2)
y + 10 = 5(x + 2)
y – 7 = ¼ (x – 20)
8x – 8y = 56
y + 6 = -1(x – 3)
