Graphing Equations Practice

Question

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Question
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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 downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 2 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.

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

(1 point)

Answer 1

To find 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. Calculate the slope (m): The slope is calculated using two points on the line. Here we can use the points (0, 2) and (1, -1).

   The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

   Using the points (0, 2) and (1, -1): \[ m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3 \]

2. Use the slope and a point to find the y-intercept (b): We can use the point (0, 2) to find b. Since we already have the slope, we can plug it into the equation: \[ y = mx + b \] Here, when \(x = 0\), \(y = 2\): \[ 2 = -3(0) + b \implies b = 2 \]

3. Write the equation in slope-intercept form: Now that we have both \(m\) and \(b\), we can write the equation: \[ y = -3x + 2 \]

Thus, the equation of the line in slope-intercept form is: \[ y = -3x + 2 \]