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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

y=3x−4

y=3x+4

y=−3x−4

1 answer

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

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

    Plugging in the values, we get: \[ m = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3 \]

  2. Use the slope to find the y-intercept \( b \): The equation of the line is now \( y = 3x + b \). To find \( b \), we can use one of the points. Let's use (0, -4): \[ -4 = 3(0) + b \Rightarrow -4 = b \]

  3. Write the equation: Now we can write the equation of the line: \[ y = 3x - 4 \]

So the correct response is: y = 3x - 4.