Use the image to answer the question.

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

3x−y=4
3 x minus y equals 4

y=3x−4
y equals 3 x minus 4

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

y=−3x−4

Answer 1

To derive 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).

From the points provided:

• Point 1: \((0, -4)\)
• Point 2: \((1, -1)\)

Step 1: Calculate the slope (m)

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: \((x_1, y_1) = (0, -4)\) and \((x_2, y_2) = (1, -1)\),

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

Step 2: Find the y-intercept (b)

Now, we can use the slope \(m = 3\) and one of the points to find \(b\). Using the point \((0, -4)\):

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

Step 3: Write the equation in slope-intercept form

Now we can substitute \(m\) and \(b\) back into the slope-intercept form:

\[ y = 3x - 4 \]

Thus, the equation of the line in slope-intercept form is:

\[ \boxed{y = 3x - 4} \]

The correct response from the options provided is y = 3x - 4.