Use the image to answer the question. Give the correct answer!

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
y equals negative 5 x plus 1

y=−5x−1
y equals negative 5 x minus 1

y=5x+1
y equals 5 x plus 1

−5x−y=−1

3 answers

y=−5x+1

Give more detail than that

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

The slope of the line can be found using the two given points (0, 1) and (1, -4). The slope formula is:

m = (y2 - y1) / (x2 - x1)

Using the coordinates from the first point (0, 1):

m = (-4 - 1) / (1 - 0) = -5

Now that we have the slope, we can use the point-slope form of a linear equation (y - y1 = m(x - x1)) to find the equation. We can use either of the given points, let's use (0, 1):

y - 1 = -5(x - 0)

y - 1 = -5x

Now, we can rewrite the equation in slope-intercept form (y = mx + b) by moving the constant term to the other side of the equation:

y = -5x + 1

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