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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 negative 3 x minus 4

y=3x−4
y equals 3 x minus 4

y=3x+4
y equals 3 x plus 4

3x−y=4

1 answer

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

  1. Calculate the slope (m): The formula for slope (m) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, (x₁, y₁) = (0, -4) and (x₂, y₂) = (1, -1). \[ m = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3 \]

  2. Find the y-intercept (b): We know that the y-intercept occurs when x = 0. From the given point (0, -4), we can see that when x = 0, y = -4. Therefore, b = -4.

  3. Write the equation in slope-intercept form: Now that we have the slope (m = 3) and the y-intercept (b = -4), we can write the equation of the line: \[ y = 3x - 4 \]

The correct answer from the options provided is: y = 3x - 4 (y equals 3 x minus 4).