Use the graph to derive the equation of the line in slope-intercept form (0,-2) and (1,3)
To find the equation of the line passing through the points (0, -2) and (1, 3) in slope-intercept form, we first need to find the slope of the line using the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Using the given points:
m = (3 - (-2)) / (1 - 0)
m = 5 / 1
m = 5
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation in slope-intercept form, which is:
y - y1 = m(x - x1)
Using the point (0, -2):
y - (-2) = 5(x - 0)
y + 2 = 5x
Subtracting 2 from both sides to isolate y:
y = 5x - 2
Therefore, the equation of the line passing through the points (0, -2) and (1, 3) in slope-intercept form is y = 5x - 2.