Question

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 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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page 16 of 17

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) using the points given.

The two points provided are:
- (0, -4)
- (1, -1)

**Step 1: Calculate the slope (m)**

The formula for the slope (m) between two points (x₁, y₁) and (x₂, y₂) is:
\[
m = \frac{y₂ - y₁}{x₂ - x₁}
\]

Using our points:
- (x₁, y₁) = (0, -4)
- (x₂, y₂) = (1, -1)

Now plug in the values:
\[
m = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3
\]

**Step 2: Use the slope to find the y-intercept (b)**

We can use one of the points to find b. We can use (0, -4):
The equation of the line in slope-intercept form is:
\[
y = mx + b
\]

Substituting m and the point (0, -4):
\[
-4 = 3(0) + b \implies -4 = b
\]

So the y-intercept (b) is -4.

**Step 3: Write the equation**

Now we substitute m and b back into the slope-intercept form:
\[
y = 3x - 4
\]

Thus, the equation of the line in slope-intercept form is:
\[
y = 3x - 4
\]

The correct response is:
**y = 3x - 4**.