Question

Graphing Linear Equations Unit Test
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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+
(
)

Answer 1

To find the equation of the line in slope-intercept form \( y = mx + b \), we first need to determine the slope \( m \) using the two points provided: Point A \((-1, 2)\) and Point B \((0, -1)\).

1. **Calculate the slope \( m \)**:
The slope \( m \) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, we can take:
- Point A as \((x_1, y_1) = (-1, 2)\)
- Point B as \((x_2, y_2) = (0, -1)\)

Plugging in the values:
\[
m = \frac{-1 - 2}{0 - (-1)} = \frac{-3}{1} = -3
\]

2. **Find the y-intercept \( b \)**:
The y-intercept occurs where \( x = 0 \). From Point B, we can see that when \( x = 0 \), \( y = -1 \). Thus, \( b = -1 \).

3. **Write the equation of the line**:
Now that we have both the slope and y-intercept, we can write the equation in slope-intercept form:
\[
y = -3x - 1
\]

So, the complete answer is:
\[
y = -3x - 1
\]