Question

Use the image to answer the question.

A coordinate plane of 4 quadrants shows x and y axes ranging from negative 3 to 3 in increments of 1. A line with arrows at each end intercepts two plotted points, A and B. Point A is plotted at left parenthesis negative 1 comma 2 right parenthesis. Point B is plotted at left parenthesis 0 comma negative 1 right parenthesis.

Write the equation of the line in slope-intercept form.

(1 point)
y=
x+
(
)
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Answer 1

To find the equation of the line that passes through points A \((-1, 2)\) and B \((0, -1)\), we first need to determine the slope \(m\) of the line and then use one of the points to write the equation in slope-intercept form \(y = mx + b\).

1. **Calculate the slope \(m\)**:

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

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

Using points A(-1, 2) and B(0, -1):

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

2. **Use the slope-intercept form**:

We have the slope \(m = -3\). Now, we can use point B \((0, -1)\) to find the y-intercept \(b\):

In the slope-intercept form, when \(x=0\), \(y=b\). Since point B is at \((0, -1)\), we see that \(b = -1\).

3. **Write the equation**:

Substituting the values of \(m\) and \(b\) into the slope-intercept form \(y = mx + b\):

\[
y = -3x - 1
\]

So the final equation of the line in slope-intercept form is:

\[
y = -3x - 1
\]