Question

Use the image to answer the question.

An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 1 comma 3 right parenthesis.

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

(1 point)
y=
x-
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Answer 1

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

1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5
\]

2. **Use the slope and one of the points to find the y-intercept (b)**. We'll use the point (0, -2):
\[
y = mx + b
\]
Substituting the point into the equation:
\[
-2 = 5(0) + b \quad \Rightarrow \quad -2 = b
\]

3. **Now plug in the slope and the y-intercept into the slope-intercept form**:
\[
y = 5x - 2
\]

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

\[
y = 5x - 2
\]