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 negative 5 x minus 1

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

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

y=−5x+1

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) of the line using the two points it passes through: (0, 1) and (1, -4).

1. Calculate the slope (m): The formula for the slope \( m \) between two points (x1, y1) and (x2, y2) is given by:

   \[ m = \frac{y2 - y1}{x2 - x1} \]

   Using the points (0, 1) and (1, -4):

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

2. Use the slope to write the equation: Now that we know the slope is -5, we can use one of the points to find the y-intercept (b). We will use the point (0, 1), where x = 0 and y = 1:

   \[ y = mx + b \] Plugging in the values we have:

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

3. Write the equation in slope-intercept form: Now that we have both m and b, we can write the equation of the line:

   \[ y = -5x + 1 \]

Therefore, the correct response is:

y = -5x + 1