Question

Derive the equation of the line in slope-intercept form.

(1,8) (0,4)

Answer 1

First, let's find the slope of the line using the formula:

m = (y2 - y1) / (x2 - x1)

Substitute the given points into the formula:

m = (4 - 8) / (0 - 1)
m = -4 / -1
m = 4

Now that we have the slope, we can use the point-slope formula to find the equation of the line:

y - y1 = m(x - x1)

Substitute in one of the given points (0,4):

y - 4 = 4(x - 0)
y - 4 = 4x

Now, we can rewrite this equation in slope-intercept form (y = mx + b):

y = 4x + 4

Therefore, the equation of the line in slope-intercept form is y = 4x + 4.