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

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

y=−5x+1
y equals negative 5 x plus 1

y=−5x−1
y equals negative 5 x minus 1

−5x−y=−1
negative 5 x minus y equals negative 1
Skip to navigation

Answer 1

To find 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: (0, 1) and (1, -4).

The formula for slope (m) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points:

• \( (x_1, y_1) = (0, 1) \)
• \( (x_2, y_2) = (1, -4) \)

Substituting the values:

\[ m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5 \]

Now that we have the slope, we can use one of the points to find the y-intercept (b). Let’s use the point (0, 1):

Using the slope-intercept form \( y = mx + b \):

\[ 1 = -5(0) + b \] \[ 1 = b \]

Now we can write the equation of the line:

\[ y = -5x + 1 \]

Therefore the correct response is:

y = −5x + 1