Use the image to answer the question.

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 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

−5x−y=−1
negative 5 x minus y equals negative 1
y=5x+1
y equals 5 x plus 1
y=−5x+1
y equals negative 5 x plus 1
y=−5x−1

Answer 1

To find the equation of the line in slope-intercept form, we first need to find the slope of the line.

The slope formula is:
m = (y2 - y1) / (x2 - x1)

Using the points (0, 1) and (1, -4) on the line:
m = (-4 - 1) / (1 - 0) = -5 / 1 = -5

The slope of the line is -5.

Next, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)

Using the point (1, -4):
y - (-4) = -5(x - 1)
y + 4 = -5x + 5
y = -5x + 1

So, the equation of the line in slope-intercept form is y = -5x + 1.

Therefore, the correct response is:
y = -5x + 1