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

Question

x-intercept: -1/2

 

y-intercept: 4

 

Give point-slope form and slope intercept form

 

Just confused how to get to that just with intercepts, please explain in detail!

 

Thanks!

Answer 1

Here's what we know:

Two points are (-½, 0) and (0, 4)

By using these points we can find the slope using rise-over-run:

(y₁ - y₂) / (x₁ - x₂)

(0 - 4) / (-½ - 0)

-4/-½

4/½

8

So the slope of the line is 8.

We have the slope and we have the y-intercept, so the slope-intercept is easy:

y = mx + b

y = 8x + 4

 

For point-slope, we just use a point on the line. We already have a couple given to us, and we'll be using the (-½, 0) in this case:

y - y₁ = m(x - x₁)

y - 0 = 8(x - (-½))

y = 8(x + ½)

Answer 2

By giving you the intercepts, they have in fact given you 2 points on the line.

x-intercept: the point where the line crosses the x-axis, or when y=0. So the point is (-1/2,0)

y-intercept: the point where the line crosses the y-axis, or when x=0. So the point is (0,4)

So you can find the slope as you usually would from these 2 points:

 

m=(y₁-y₂)/(x₁-x₂)

m=(0-4)/(-1/2)

m=8

 

Now you can form your point slope form, which is:

y-y₁=m(x-x₁)

y-0=8(x+1/2)

y=8(x+1/2)

 

Then your slope-intercept form is:

y=mx+b (b is the y-intercept) 

y=8x+4