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 negative 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) of the line and then find the y-intercept (b).

1. Calculate the slope (m): The slope formula is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (0, -4) and (1, -1): \[ m = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3 \]

2. Use the slope and a point to find the y-intercept (b): We can use the slope-intercept form and one of the points (let's use (0, -4)): \[ y = mx + b \] Substituting in the point (0, -4): \[ -4 = 3(0) + b \] Which simplifies to: \[ b = -4 \]

3. Write the equation: Now we have the slope (m = 3) and the y-intercept (b = -4). Therefore, the equation of the line in slope-intercept form is: \[ y = 3x - 4 \]

So the correct response is:

y = 3x - 4.