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-

Answer 1

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

1. **Find the slope (m)**:
The slope \(m\) is calculated using the formula:

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

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

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

Plugging in the values:

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

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

3. **Write the equation of the line**:
Now that we have the slope and the y-intercept, we can write the equation in slope-intercept form:

\[
y = 5x - 2
\]

Thus, the equation of the line is:

\[
y = 5x - 2
\]