Intercepts

Objective: To graph a linear equation using the x- and y-intercepts or using

the slope and y-intercept.

5-Minute CheckFind the slope of the line that contains each pair of points.

1. C(-4, -2), D(5, 3)

5-Minute CheckFind the slope of the line that contains each pair of points.

1. C(-4, -2), D(5, 3) 5/9

5-Minute CheckFind 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-Minute CheckFind 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

5-Minute CheckFind 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)

5-Minute CheckFind 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 CheckFind 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)

5-Minute CheckFind 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-Minute CheckFind 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)

5-Minute CheckFind 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

What is an interception in football?

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.

InterceptsThe line graphed below crosses both axes.

x-intercept

y-intercept

The line graphed crosses the x-axis at (5, 0). Therefore the x-intercept is 5. Note that the corresponding y-coordinate is 0.

The line crosses the y-axis at (0, 2). So the y-intercept is 2. Note that the corresponding x-coordinate is 0.

6

5

4

3

2

1

01 2 3 4 5 6

y-intercept

x-intercept

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.

InterceptsExample 1Find the x-intercept and y-intercept for y = 3/2x – 6. Then graph the equation using the x- and y-intercepts.

x-intercept:y = 3/2x – 60 = 3/2x – 6 0 + 6 = 3/2x – 6 + 6 6 = 3/2x 6*2/3 = 3/2*2/3x 4 = xThe x-intercept is 4.The ordered pair is (4,0).

y-intercept:y = 3/2x – 6y = 3/2*0 – 6 y = – 6

The y-intercept is -6.The ordered pair is (0,-6).

InterceptsThe 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

-4

-5

-6

0

-1

-2

-3

InterceptsThe 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

-4

-5

-6

0

-1

-2

-3

InterceptsThe 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

-4

-5

-6

0

-1

-2

-3

InterceptsThe 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

-4

-5

-6

0

-1

-2

-3

We can check our work by selecting a point on the line, (2,-3) to see if we are correct.

y = 3/2x – 6

– 3 = 3/2(2) – 6

– 3 = 3 – 6

– 3 = – 3

Intercepts

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

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?

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?