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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 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 minus 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 plus 4
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Answer 1

To find the equation of the line in slope-intercept form \(y = mx + b\), we first need to determine the slope \(m\) of the line using the two given points \((0, -4)\) and \((1, -1)\).

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting in the values from the points:

\[ m = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1 - 0} = \frac{3}{1} = 3 \]

Now we have the slope \(m = 3\). Next, we use one of the points to find the y-intercept \(b\). We can use the point \((0, -4)\).

Using the slope-intercept form \(y = mx + b\):

\[ -4 = 3(0) + b \]

This simplifies to:

\[ -4 = b \]

Now that we have the slope and y-intercept, we can write the equation of the line:

\[ y = 3x - 4 \]

So, the correct response is:

y = 3x - 4