Graphing Equations Quick Check

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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 upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.

Using the graph, derive the equation of the line in slope-intercept form.

(1 point)
Responses

y=3x+4
y equals 3 x plus 4

y=−3x−4
y equals negative 3 x minus 4

3x−y=4
3 x minus y equals 4

y=3x−4
y equals 3 x minus 4
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Answer 1

To find the equation of the line passing through the points (0, -4) and (1, -1), we will first determine the slope and then use the slope-intercept form \(y = mx + b\).

1. Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3 \]

2. Use the slope-intercept form: We know the slope \(m = 3\) and can also substitute one of the points to find \(b\). We'll use (0, -4): \[ y = mx + b \Rightarrow -4 = 3(0) + b \Rightarrow -4 = b \]

3. Write the equation: Now we can write the equation in slope-intercept form: \[ y = 3x - 4 \]

Therefore, the correct response is: y = 3x - 4.