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

Question

(0,-2) and (3,0)

Answer 1

First, we need to calculate the slope of the line using the formula:

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

where (x1, y1) = (0, -2) and (x2, y2) = (3, 0).

m = (0 - (-2)) / (3 - 0)
m = 2 / 3

Now that we have the slope, we can use the point-slope form of a linear equation to derive the equation in slope-intercept form:

y - y1 = m(x - x1)

Using the point (0, -2):

y - (-2) = (2/3)(x - 0)
y + 2 = (2/3)x

Now, we can rewrite this equation in slope-intercept form:

y = (2/3)x - 2