Question

Write the equation of the line in fully simplified slope intercept form.

Answer 1

y = 3/4x + 7

In-depth explanation:

Hi! This question is asking us to write the equation of the line in fully simplified slope intercept form.

Given

• Two points on the graph (-8,1) and (-4,4)

_____________

Solving for:

• The line's slope

______________

SLOPE FORMULA

`\boxed{\bf{m=(y_2-y_1)/(x_2-x_1)}}`

______________

Plug in the data

`\bf{m=(4-1)/(-4-(-8))}`

`\bf{m=(3)/(-4+8)}`

`\bf{m=(3)/(4)}`

_____________

Y-INTERCEPT

The equation of the line is,
`\sf{y=(3)/(4)x+b}`.

We need to find b, so we take a point & plug its coordinates into the equation. I take (-4,4).

`\bf{4=(3)/(4)*(-4)+b}`

`\bf{4=-3+b}`

`\bf{4+3=b}`

`\bf{7=b}`

∴ Equation: y = 3/4x + 7