Question

A line passes through the point (-8, 7) and has a slope of negative 3/4Write an equation in slope-intercept form for this line.

Answer 1

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

Explanation:

We do not have enough information for slope intercept form. But we can use the point-slope formula to find the information. The formula is
`y -y_(1) =m(x -x_(1))` where we substitute a point (x,y) for
`(x_(1),y_(1))`.

We have m=-3/4 and (-8, 7). We input m and
`x_(1) =-8\\y_(1)=7`.

`y-7=-(3)/(4) (x-(-8))\\y-7=-(3)/(4) (x+8)`

We now simplify the parenthesis and solve for y.

`y-7=-(3)/(4) (x+8)\\y-7=-(3)/(4)x+-(3)/(4) (8)`

We convert 8 into a fraction with 1 as the denoinator.

`y-7=-(3)/(4)x+-(3)/(4) ((8)/(1) )\\y-7=-(3)/(4)x+-(24)/(4)\\y-7=-(3)/(4)x+-6`

We add 7 to both sides to isolate y,

`y-7+7=-(3)/(4)x+-6+7\\y=-(3)/(4)x+1`

This is slope intercept form. The line as slope -3/4 and y-intercept (0,1) or b=1.