Question

Use the image to answer the question. Use the graph to derive the equation of the line in slope-intercept form. (1 point) (1,3) (0,-2)

Answer 1

To derive the equation of the line in slope-intercept form (y = mx + b) using the points (1, 3) and (0, -2), follow these steps:

1. **Determine the slope (m)**:
The formula for slope (m) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (1, 3) and (0, -2):
\[
m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5
\]

2. **Use the point (0, -2) to find the y-intercept (b)**:
In slope-intercept form, the y-intercept is the value of y when x = 0. The point (0, -2) indicates that when x is 0, y is -2. Thus, b = -2.

3. **Write the equation in slope-intercept form**:
Now we can substitute m and b into the slope-intercept form.
\[
y = mx + b \implies y = 5x - 2
\]

Thus, the equation of the line in slope-intercept form is:
\[
y = 5x - 2
\]