Question

Use the given conditions to write an equation for the line in point-slope form and

in slope-intercept form.
Passing through (1,8) with x-intercept 4
Write an equation for the line in point-slope form.
(Simplify your answer. Use integers or fractions for any numbers in the equation.)

Answer 1

`Point-slope -form:\\y-8=-(8)/(3)(x-1)\\Slope-intercept-form:\\y=-(8)/(3)x+ (32)/(3)`

Explanation:

Point-slope form:

`y-y_(1) = m(x-x_(1))`

Slope-intercept form:

`y=mx+b`

What we are given:

A point = (1,8)

x-intercept = 4

What we are missing:

Slope = "m"

y-intercept = "b" in the slope-intercept form

How to find slope:

We need two points, we are already given one, (1,8).

A "hidden" second point would be the x-intercept. Since we know that y=0 in the x-intercept, we can say that another point on the line is (4,0).

So now we have 2 points, (1,8) and (4,0).

Slope formula: Rise (y) / Run (x)

`(8-0)/(1-4)= -(8)/(3)`

Now we have the slope, we can figure out the y-intercept using one of the points, here I use 1,8.

`y=mx+b\\y=-(8)/(3) x+b\\8=-(8)/(3) *(1)+b\\8=-(8)/(3) +b\\(24)/(3) =-(8)/(3) +b\\(32)/(3) =b\\\\b=(32)/(3)`

Now, we know the y-intercept and the slope.

We can substitute all values know.