Question

se the image to answer the 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 plus 1

y=−5x−1
y equals negative 5 x minus 1

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

y=5x+1
y equals 5 x plus 1
Skip to navigation

Answer 1

To determine the equation of the line in slope-intercept form (y = mx + b), we need to calculate the slope (m) first and then find the y-intercept (b).

1. **Calculate the slope (m)**:
We can use the two points given: (0, 1) and (1, -4). The slope formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the values:
\[
m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5
\]

2. **Use the point-slope form to find the equation**:
We can use the slope-intercept form y = mx + b, where we now know that m = -5. We'll use the point (0, 1) to find b (the y-intercept):
\[
1 = -5(0) + b \implies 1 = b
\]

3. **Write the equation**:
Now we have both m and b:
\[
y = -5x + 1
\]

Thus, the equation of the line in slope-intercept form is:
\[
y = -5x + 1
\]

The correct response is:
**y = −5x + 1**.