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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 downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 1 right parenthesis and left parenthesis 1 comma negative 4 right parenthesis.

Write the equation of the line in slope-intercept form.

(1 point)
Responses

y=5x+1

−5x−y=−1

y=−5x+1

y=−5x−1

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. Find the slope (m): We have two points: (0, 1) and (1, -4). The formula for the slope is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points (0, 1) as (x_1, y_1) and (1, -4) as (x_2, y_2): \[ m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5 \]

  2. Find the y-intercept (b): Using the point (0, 1) which is on the line, we can directly see that when x = 0, y = 1. Hence, the y-intercept (b) is 1.

Now, we can write the equation of the line: \[ y = -5x + 1 \]

Thus, the equation of the line in slope-intercept form is: \[ \text{y = -5x + 1} \]

The correct response is y = -5x + 1.