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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

1 answer

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.