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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+
(
)

1 answer

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: \[ y = -3x - 1 \]