Question

(0,-2)
(1,3)

Use the graph to derive the equation of the line in slope-Intercept form.

Answer 1

To derive the equation of the line in slope-intercept form \(y = mx + b\), we first need to determine the slope (\(m\)) using the two given points: \((0, -2)\) and \((1, 3)\).

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Now, substituting our points into this formula:

- Let \((x_1, y_1) = (0, -2)\)
- Let \((x_2, y_2) = (1, 3)\)

Calculating the slope:

\[
m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5
\]

Now that we have the slope \(m = 5\), we can use one of the points to find the y-intercept \(b\). Since one of the points is \((0, -2)\), we can directly see that when \(x = 0\), \(y = -2\). Thus, the y-intercept \(b = -2\).

Therefore, the equation of the line in slope-intercept form is:

\[
y = 5x - 2
\]