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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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1 answer

To find the equation of the line in slope-intercept form (y = mx + b), we first need to calculate the slope (m) of the line using the two points provided: (0, -4) and (1, -1).

  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):

  • \(x_1 = 0\), \(y_1 = -4\)

  • \(x_2 = 1\), \(y_2 = -1\)

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

  1. Now, find the y-intercept (b):

    Since the point (0, -4) lies on the line, it provides us the y-intercept directly. The y-intercept (b) is -4.

  2. Write the equation:

    Now we can substitute the slope and y-intercept into the slope-intercept equation \(y = mx + b\): \[ y = 3x - 4 \]

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