Question

Use the graph to write the equation of the line in slope-intercept ( y=mx+b
) form.
(1, 3)
(0, -2)


(1 point)
The equation of the line in y=mx+b
form is:

Answer 1

To find the equation of the line in slope-intercept form \( y = mx + b \), we first need to determine the slope \( m \) and the y-intercept \( b \).

Given the points \( (1, 3) \) and \( (0, -2) \):

1. **Calculate the slope \( m \)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let's take \( (x_1, y_1) = (0, -2) \) and \( (x_2, y_2) = (1, 3) \):
\[
m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5
\]

2. **Identify the y-intercept \( b \)**:
The y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From the point \( (0, -2) \), we see that \( b = -2 \).

3. **Write the equation**:
Substituting the values of \( m \) and \( b \) into the slope-intercept form gives us:
\[
y = 5x - 2
\]

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