Question

p1 = 0,1
p2 = 1,-4
Write the equation of the line
in slope-intercept form.
(1 point)
y = 5x + 1
y = −5x − 1
y = −5x + 1
−5x − y = −1

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b) that passes through the points \( p1(0, 1) \) and \( p2(1, -4) \), we can follow these steps:

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \( (x_1, y_1) = (0, 1) \) and \( (x_2, y_2) = (1, -4) \):
\[
m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5
\]

2. **Use the point-slope form** of the line equation with one of the points to find the y-intercept (b). We can use point \( p1(0, 1) \):
\[
y - y_1 = m(x - x_1)
\]
Plugging in \( m = -5 \), \( (x_1, y_1) = (0, 1) \):
\[
y - 1 = -5(x - 0)
\]
\[
y - 1 = -5x
\]
\[
y = -5x + 1
\]

Now we have the equation of the line in slope-intercept form:
\[
y = -5x + 1
\]

The correct option from your list is:
**y = −5x + 1.**