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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 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)
Remaining Attempts : 3
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Answer 1

To write the equation of a 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 formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points \((0, 2)\) and \((1, -1)\):

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

   Substitute these values: \[ m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3 \]

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

3. Write the equation: Now, substitute the slope \(m\) and the y-intercept \(b\) into the slope-intercept form: \[ y = -3x + 2 \]

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