Question

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Graphing Equations Quick Check
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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

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

3x−y=4
3 x minus y equals 4

y=−3x−4
y equals negative 3 x minus 4

y=3x−4

Answer 1

To derive the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).

1. **Identify two points on the line**: From the description, the line passes through the points (0, -4) and (1, -1).

2. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using (0, -4) as (x1, y1) and (1, -1) as (x2, y2):
\[
m = \frac{-1 - (-4)}{1 - 0} = \frac{3}{1} = 3
\]

3. **Write the slope-intercept equation**: Since we have the slope (m = 3), we can use one of the points to find the y-intercept (b). Let's use (0, -4):
\[
y = mx + b
\]
Plug in m and the point (0, -4):
\[
-4 = 3(0) + b \implies b = -4
\]

4. **Combine the slope and y-intercept**: The equation in slope-intercept form is:
\[
y = 3x - 4
\]

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