Derive the equation of the line in slope-intercept form. (1 point) points are at (0,-2)&(3,0)

Answer 1

To find the equation of the line in slope-intercept form, we first need to find the slope of the line using the given points (0, -2) and (3, 0).

The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

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

In this case, (x1, y1) = (0, -2) and (x2, y2) = (3, 0). So, we have:

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

Now that we have the slope, we can use the point-slope form of the equation of a line to write the equation of the line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Using the point (0, -2), we have:

-2 = (2/3)(0) + b
-2 = b

So, b = -2. Therefore, the equation of the line in slope-intercept form is:

y = (2/3)x - 2