Question

The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y−4=1/4(x−8) . What is the slope-intercept form of the equation for this line?

Answer 1

y = 1/4x + 2

Explanation:

The general form of the point-slope form is

`y-y_(1)=m(x-x_(1))`, where (x1, y1) are any point on the line and m is the slope

We can convert the point-slope form of an equation into the slope-intercept form by isolating y on the left-hand side of the equation. To do this, we'll have to distribute to m to both x and -x1 and add y1 to both sides:

`y-4=1/4(x-8)\\y-4=1/4x-2\\y=1/4x+2`

Now, we can check the the slope-intercept form is correct by plugging in the (0, 2) for x and y and also (8, 4) for x and y. If the equation is true, then we've correctly converted the point-slope form to the slope-intercept form:

Plugging in (0, 2) for x and y in the slope-intercept form:

`2=1/4(0)+2\\2=2`

Plugging in (8, 4) for x and y in the slope-intercept form:

`4=1/4(8)+2\\4=2+2\\4=4`