use the graph to derive the equation of the line in slope-intercept form.

Question

graph: (0,-2) ,(1,3)

Answer 1

To find the equation of the line in slope-intercept form, we first need to find the slope of the line.

Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (3 - (-2)) / (1 - 0)
Slope (m) = 5 / 1
Slope (m) = 5

Now that we have the slope, we can use one of the points on the line to find the y-intercept.

Using the point (0, -2):
y = mx + b
-2 = 5(0) + b
-2 = b

Therefore, the y-intercept (b) is -2.

Now we have the slope (m = 5) and the y-intercept (b = -2), so the equation of the line in slope-intercept form is:
y = 5x - 2