Question

Find the x- and y- intercepts of the line with the given equation

-6x+8y=-36

Answer 1

x-intercept (6,0)

y-intercept (0,-4.5)

Explanation:

the x-intercept will be when y=0

and the y-intercept will be when x=0

so

`y=0\\\\-6x+8(0)=-36\\\\-6x=-36\\\\x=6`

so the x intercept will be at (6,0)

`x=0\\\\-6(0)+8y=-36\\\\8y=-36\\\\y=-(9)/(2)\\\\y=-4.5`

so the y intercept will be at (0,-4.5)

Answer 2

Y int at

(

0

,

3

2

)

X int at

(

3

,

0

)

Explanation:

The line is easier to visualize when the equation is in slope-intercept form:

4

x

+

8

y

=

12

Divide each side by 4:

x

+

2

y

=

3

2

y

=

−

x

+

3

y

=

−

1

2

x

+

3

2

Y-intercept (plug in 0 for x):

y

=

−

1

2

(

0

)

+

3

2

y

=

3

2

X-intercept (plug in 0 for y):

0

=

−

1

2

x

+

3

2

−

3

2

=

−

1

2

x

x

=

3