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 negative 5 x minus 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 (y = mx + b), we first need to determine the slope (m) of the line that passes through the points (0, 1) and (1, -4).

1. Calculate the slope (m): The slope formula is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (0, 1) and (1, -4):

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

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

2. Use the slope and one of the points to find the y-intercept (b): We can use the point (0, 1) to find b: \[ y = mx + b \] Plugging in the values, where \(y = 1\), \(m = -5\), and \(x = 0\): \[ 1 = -5(0) + b \] \[ 1 = b \]

3. Write the equation in slope-intercept form: Now we have \(m = -5\) and \(b = 1\): \[ y = -5x + 1 \]

Thus, the equation of the line in slope-intercept form is \(y = -5x + 1\).

The correct response from the options provided is: y = -5x + 1 (y equals negative 5 x plus 1).