Question

Write an equation for the line in slope intercept form

Answer 1

`y=-(3)/(4)x+4`

Explanation:

Slope-intercept form: y = mx + b

Slope (m):
`(y_2-y_1)/(x_2-x_1)`

Use two points on the line to find the slope (m)

(4, 1) and (-4, 7)

`m=(7-1)/(-4-4) \\\\m=(6)/(-8)\\\\m=-(6/2)/(-8/2)\\\\m=-(3)/(4)`

y = mx + b

`y=-(3)/(4)x+b`

Now we find b, using either (4, 1) or (-4, 7)

(4, 1)

`y=-(3)/(4)x+b\\\\1=-(3)/(4)(4)+b\\\\1=-3+b\\+3 +3\\\\4=b`

`y=-(3)/(4)x+b== > y=-(3)/(4)x+4`

Check your answer using either of the points:

`(4,1)\\y=-(3)/(4)x+4\\\\1=-(3)/(4)(4)+4\\\\1=-3+4\\\\1=1`

This statement is true

Therefore, our final answer is
`y=-(3)/(4)x+4`

Hope this helps!