Question

Use the image to answer the question.
(0, 1), (1, -4)
Write the equation of the line in slope-intercept form.
A. -5x - y = -1
B. y = 5x + 1
C. y = -5x - 1
D. y = -5x + 1

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b) using the given points, we can first calculate the slope (m) using the formula:

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

The points given are (0, 1) and (1, -4). Let's use these points:

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

Now, we can plug in the values:

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

So the slope \( m = -5 \).

Now we use the slope-intercept form equation \( y = mx + b \) and substitute \( m \) and one of the points to find \( b \). We'll use the point (0, 1):

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

Thus, the equation of the line in slope-intercept form is:

\[ y = -5x + 1 \]

So the correct answer is:

**D. y = -5x + 1**