Question

Graphing Equations Quick Check
3 of 53 of 5 Items



Question
Use 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

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

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

y=−5x−1
y equals negative 5 x minus 1

Answer 1

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

1. **Finding the slope (m)**:
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 1) and (1, -4):
\[
m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5
\]

2. **Finding the y-intercept (b)**:
We know the equation now takes the form:
\[
y = -5x + b
\]
We can substitute one of the points to find b. Using the point (0, 1):
\[
1 = -5(0) + b \implies b = 1
\]

3. **Putting it all together**:
The equation of the line is:
\[
y = -5x + 1
\]

Thus, the correct answer is:
**y = −5x + 1**.