use the Graph derive the equation of the line in slope intercept form with points 0,-2 and 1,3

Answer 1

First, we need to find the slope of the line passing through the points (0, -2) and (1, 3).

slope = (change in y) / (change in x)
slope = (3 - (-2)) / (1 - 0)
slope = 5 / 1
slope = 5

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line passing through the points.

y - y1 = m(x - x1)

Using the point (0, -2) and the slope m = 5:

y - (-2) = 5(x - 0)
y + 2 = 5x

Now, rearrange the equation into slope-intercept form (y = mx + b):

y + 2 = 5x
y = 5x - 2

Therefore, the equation of the line passing through the points (0, -2) and (1, 3) is y = 5x - 2.