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Definition:
xโ intercept: the point where the line crosses (or intercepts) the x -axis
yโ intercept: : the point where the line crosses (or intercepts) the y -axis
Types of Linear:
Steps for graphing a Linear Equation in Two Variables
๏ Step 1. Find x -intercept and y -intercept by substituting x = 0 and y = 0
๏ Step 2. Plot intercepts obtained in the step 1
๏ Step 3: Draw a line through these two points
Positive Slope Negative Slope Slope = 0: y=b Undefined slope: x=a
y -int: (0, y )
x -int: ( x , 0)
Example
Plot intercepts to graph the
equation: ๐ฆ = 2 ๐ฅ + 4
(Solution)
Step 1: Find intercepts
y -intercept: (0, y )
Thus, y - int: (0, 4)
x -intercept: ( x , 0)
Thus, x -int: (โ2, 0)
Step 2: Plot intercept obtained in the step 2, (0, 4) and (โ2, 0)
Step 3: Draw a line through these two points, (0, 4) and (โ2, 0)
TI-83/84:
> > 2X +4 > >
TI-89:
> tblStart: -10 / โtbl: 0.5 > > 2X+4 >
x -int: (-2, 0) y -int: (0, 4)
2nd WINDOW 2nd GRAPH
2nd WINDOW Y= 2nd MODE 2nd GRAPH
F4 F1 2nd F
(Solution 3) x -intercept is the point where the graph intercepts the x -axis. The horizontal line does not cross the x -axis. y -intercept is the point where a line crosses the y -axis. The given graph crosses at 7 on the y -axis. (Solution 4) Step 1: Find x -intercept Step 2: Find y -intercept Substitute y = 0 Substitute x = 0 ๐ฅ + ๐ฆ= 7 ๐ฅ + ๐ฆ= 7 ๐ฅ + ( 0 )= 7 ( 0 ) + ๐ฆ= 7 ๐ฅ = 7 ๐ฆ= 7 So, x -intercept is (7, 0) So, y -intercept is (0, 7) Step 3: Plot the obtained points. The graph is shown below
(Solution 5) Step 1: Find x -intercept Step 2: Find y -intercept Substitute y = 0 Substitute x = 0 7 ๐ฅ โ 3 ๐ฆ= โ 21 7 ๐ฅ โ 3 ๐ฆ= โ 21 7 ๐ฅ โ 3 ( 0 )= โ 21 7 ( 0 ) โ 3 ๐ฆ= โ 21 7 ๐ฅ = โ 21 โ 3 ๐ฆ= โ 21 7 ๐ฅ 7
So, x -intercept is (โ3, 0) So, y -intercept is (0, 7) Step 3: Plot the obtained points. The graph is shown below. (Solution 6) Step 1: Find x -intercept Step 2: Find y -intercept Substitute y = 0 Substitute x = 0 45 ๐ฆ= 360 โ 180 ๐ฅ 45 ๐ฆ= 360 โ 180 ๐ฅ 45 ( 0 )= 360 โ 180 ๐ฅ 45 ๐ฆ= 360 โ 180 ( 0 ) 0 = 360 โ 180 ๐ฅ 45 ๐ฆ= 360 โ 360 โ 360 45 ๐ฆ 45
So, x -intercept is (2, 0) So, y -intercept is (0, 8) Step 3: Plot the obtained points. The graph is shown below
(Solution 9) Step 1: Find x -intercept Step 2: Find y -intercept Substitute y = 0 Substitute x = 0 9 ๐ฅ โ 3 ๐ฆ= 9 9 ๐ฅ โ 3 ๐ฆ= 9 9 ๐ฅ โ 3 ( 0 )= 9 9 ( 0 ) โ 3 ๐ฆ= 9 9 ๐ฅ = 9 โ 3 ๐ฆ= 9 9 ๐ฅ 9
So, x -intercept is (1, 0) So, y -intercept is (0, โ3) Step 3: Plot the obtained points. The graph is shown below. (Solution 10) A horizontal line is given by y = b , where b is the y -intercept. The y -intercept, b , is the y -coordinate of the point at which the graph crosses or touches the y -axis. Since the graph intercepts at 5 on y -axis, b = 5 Therefore, the equation for the line is y = 5. (Solution 10) A vertical line is given by x = a , where a is the x -intercept. The x -intercept, a , is the x -coordinate of the point at which the graph crosses or touches the x -axis. Since the graph intercepts at โ 4 on x -axis, a = โ 4 Therefore, the equation for the line is x = โ4.
