The document discusses intercepts in linear equations. It defines an x-intercept as the x-coordinate where the graph of the linear equation crosses the x-axis. The y-intercept is defined as the y-coordinate where the graph crosses the y-axis. To find the intercepts of a linear equation, set y=0 and solve for x to find the x-intercept, or set x=0 and solve for y to find the y-intercept. An example finds the intercepts of y=3/2x - 6 by setting each variable equal to 0 and solving, finding the x-intercept to be 4 and the y-intercept to be -6.

1. Intercepts
Objective: To graph a linear equation
using the x- and y-intercepts or using
the slope and y-intercept.

2. 5-Minute Check
Find the slope of the line that contains each pair of points.
1. C(-4, -2), D(5, 3)

3. 5-Minute Check
Find the slope of the line that contains each pair of points.
1. C(-4, -2), D(5, 3) 5/9

4. 5-Minute Check
Find the slope of the line that contains each pair of points.
1. C(-4, -2), D(5, 3) 5/9
2. H(1, 4), S(5, -2)

5. 5-Minute Check
Find the slope of the line that contains each pair of points.
1. C(-4, -2), D(5, 3) 5/9
2. H(1, 4), S(5, -2) -3/2

6. 5-Minute Check
Find the slope of the line that contains each pair of points.
1. C(-4, -2), D(5, 3) 5/9
2. H(1, 4), S(5, -2) -3/2
3. G(0, 7), B(2, -7)

7. 5-Minute Check
Find the slope of the line that contains each pair of points.
1. C(-4, -2), D(5, 3) 5/9
2. H(1, 4), S(5, -2) -3/2
3. G(0, 7), B(2, -7) -7

8. 5-Minute Check
Find the slope of the line that contains each pair of points.
1. C(-4, -2), D(5, 3) 5/9
2. H(1, 4), S(5, -2) -3/2
3. G(0, 7), B(2, -7) -7
4. J(0, 0), W(4, -4)

9. 5-Minute Check
Find the slope of the line that contains each pair of points.
1. C(-4, -2), D(5, 3) 5/9
2. H(1, 4), S(5, -2) -3/2
3. G(0, 7), B(2, -7) -7
4. J(0, 0), W(4, -4) -1

10. 5-Minute Check
Find the slope of the line that contains each pair of points.
1. C(-4, -2), D(5, 3) 5/9
2. H(1, 4), S(5, -2) -3/2
3. G(0, 7), B(2, -7) -7
4. J(0, 0), W(4, -4) -1
5. R(-4, -4), F(-5, -3)

11. 5-Minute Check
Find the slope of the line that contains each pair of points.
1. C(-4, -2), D(5, 3) 5/9
2. H(1, 4), S(5, -2) -3/2
3. G(0, 7), B(2, -7) -7
4. J(0, 0), W(4, -4) -1
5. R(-4, -4), F(-5, -3) -1

12. What is an interception in football?

13. Intercepts
Learning the Concept
The graph of a linear function may cross either the x-
axis, the y-axis, or both axes.
The x-intercept is the x-coordinate of the point
where the graph crosses the x-axis.
The y-intercept is the y-coordinate of the point
where the graph crosses the y-axis.

14. Intercepts
The line graphed below crosses both axes.
x-intercept The line graphed crosses the 6
x-axis at (5, 0). Therefore the 5
x-intercept is 5. Note that the 4
corresponding y-coordinate is 0. 3 y-intercept
2
y-intercept The line crosses the y-axis at 1
0
(0, 2). So the y-intercept is 2. 1 2 3 4 5 6
Note that the corresponding x-intercept
x-coordinate is 0.

15. Intercepts
From the previous slide, we learned that the y-
coordinate for the point of the x-intercept is 0.
We also learned that the x-coordinate for the point of
the y-intercept is 0.
So, to solve for the x-intercept for an equation, we
let the y-value be 0 and then solve for x.
Also to solve for the y-intercept for an equation, we
let the x-value be 0 and then solve for y.

16. Intercepts
Example 1
Find the x-intercept and y-intercept for y = 3/2x – 6.
Then graph the equation using the x- and y-intercepts.
x-intercept: y-intercept:
y = 3/2x – 6 y = 3/2x – 6
0 = 3/2x – 6 y = 3/2*0 – 6
0 + 6 = 3/2x – 6 + 6 y= –6
6 = 3/2x
6*2/3 = 3/2*2/3x
4=x The y-intercept is -6.
The x-intercept is 4. The ordered pair is (0,-6).
The ordered pair is (4,0).

17. Intercepts
The points were (4, 0) and (0, -6). We now graph the
intercepts and draw the line that contains them.
1 2 3 4 5 6 7 8
0
-1
-2
-3
-4
-5
-6

18. Intercepts
The points were (4, 0) and (0, -6). We now graph the
intercepts and draw the line that contains them.
1 2 3 4 5 6 7 8
0
-1
-2
-3
-4
-5
-6

19. Intercepts
The points were (4, 0) and (0, -6). We now graph the
intercepts and draw the line that contains them.
1 2 3 4 5 6 7 8
0
-1
-2
-3
-4
-5
-6

20. Intercepts
The points were (4, 0) and (0, -6). We now graph the
intercepts and draw the line that contains them.
We can check our work by
selecting a point on the line, 0
1 2 3 4 5 6 7 8
(2,-3) to see if we are correct. -1
-2
y = 3/2x – 6
-3
– 3 = 3/2(2) – 6 -4
-5
–3=3–6 -6
–3=–3

21. Intercepts
If we already have a line on the graph, how will we be able to
determine the x- and y-intercepts?

22. Intercepts
If we already have a line on the graph, how will we be able to
determine the x- and y-intercepts?
What are the intercepts?

23. Intercepts
If we already have a line on the graph, how will we be able to
determine the x- and y-intercepts?
What is the slope
of this line?