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

y=3x+4
y equals 3 x plus 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 minus 4
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Answer 1

Bot GPT 4-o mini answered
5 days ago

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

Step 1: Find the slope (m)

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

Using the points (0, -4) and (1, -1):

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

Substituting these values into the slope formula: \[ m = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3 \]

Step 2: Find the y-intercept (b)

Now that we have the slope \(m = 3\), we can use one of the points to find b. We'll use the point (0, -4): \[ y = mx + b \to -4 = 3(0) + b \to -4 = b \]

So, the y-intercept \(b = -4\).

Step 3: Write the equation of the line

Now we can write the equation of the line using the slope-intercept form: \[ y = 3x - 4 \]

Final Answer: The equation of the line in slope-intercept form is: \[ \text{y = 3x - 4} \]

So the correct response is y=3x−4.