X and Y Intercepts. X and Y Intercepts Essential Questions How can x-intercepts and y-intercepts be...

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X and Y Intercepts

Transcript of X and Y Intercepts. X and Y Intercepts Essential Questions How can x-intercepts and y-intercepts be...

X and Y Intercepts

X and Y Intercepts Essential Questions

How can x-intercepts and y-intercepts be determined?

How can equations be graphed using intercepts?

Y intercept

• The y-intercept is the point where a line crosses the y axis.

• At this point the value of x is 0.

• To find the y-intercept, plug 0 in for x in the linear equation and solve for y.

• y = 3x - 6 (0, -6)

y = 3(0) – 6

y = -6

X intercept

• The x-intercept is the point where a line crosses the x axis.

• At this point the value of y is 0.• To find the x-intercept, plug 0

in for y in the linear equation and solve for y.

• y = 3x - 6 (2, 0)

0 = 3x – 6

+6 +6

6 = 3x

2 = x

Example of Finding Intercepts

-16x + 8y = -16

y-intercept x = 0

-16(0) + 8y = -16

8y = -16

y = -2

x-intercept y = 0

-16x + 8(0) = -16 -16x = -16

x = 1

y-intercept = -2

x-intercept = 1

Example of Finding Intercepts

3x + 4y = 12

y-intercept x = 0

3(0) + 4y = 12

4y = 12

y = 3

x-intercept y = 0

3x + 4(0) = 12

3x = 12

x = 4

y –intercept = 3

x-intercept = 4

Example of Finding Intercepts

• y = 2x – 2

y-intercept x =0

In this case the equation is written in slope-intercept form (y = mx + b); therefore, the -2 is the “b” or y-intercept

x-intercept y = 0

0= 2x – 2

2 = 2x

1 = xx-intercept = 1

Find the Equation of the LineGiven the x- and y - intercepts

• Write the intercepts as ordered pairs.The x-intercept 4 is the ordered pair (4, 0).The y-intercept -2 is the ordered pair (0, -2).

• Calculate the slope.

• Substitute the slope and the y-intercept (b) into the slope-intercept formula.

Example

Write the equation of the line with x-intercept 3 and y-intercept 2.

x-intercept 3 = (3, 0); y-intercept 2 = (0, 2)

Slope:

1

2 1

2 0

0 32 2

3 3

2=y y

mx x

m

m

y = mx + b

22

3y x