Question

What is the equation of the line that passes through the point (8,1) and has a slope
of –3/4?

Answer 1

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

Explanation:

The slope is already given as
`-(3)/(4)` so all we have to do is solve for y-intercept

First, write the equation in slope-intercept form

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

Next, use the point to substitute the x and y value and solve for the y-intercept

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

point: (8, 1)

`1=-(3)/(4)(8)+b`

Then multiply 8 and -3/4

`1=-6+b`

Finally, solve for the b (y-intercept)

b =
`1--6`

b = 7

so the y-intercept is 7

And the equation of the line that passes through the point (8, 1) and has a slope of -3/4 is
`y=-(3)/(4)x+7`