Use the image to answer the question.

Question

Use the image to answer the 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 negative 3 x minus 4

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

y=3x−4
y equals 3 x minus 4

Answer 1

Bot GPT 4-o mini answered
3 hours ago

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

Calculate the slope (m):

The formula for slope is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Here, we can take:
- \( (x_1, y_1) = (0, -4) \)
- \( (x_2, y_2) = (1, -1) \)
Plugging in these values gives: \[ m = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3 \]
Use point-slope form to find the y-intercept (b):

We can use one of the points to find the y-intercept. Using the point (0, -4): \[ y = mx + b \] Substituting \( m = 3 \) and \( (0, -4) \): \[ -4 = 3(0) + b \ -4 = b \]
Write the equation in slope-intercept form:

Now that we have the slope \( m = 3 \) and the y-intercept \( b = -4 \), we can write the equation: \[ y = 3x - 4 \]

Thus, the correct response is:

y = 3x - 4