Question

Write the equation of the line, in slope intercept form (
), through the following two points.

0,1
8,0

Answer 1

To find the equation of the line in slope-intercept form \( y = mx + b \), we first need to calculate the slope \( m \) using the two given points: \( (0, 1) \) and \( (8, 0) \).

The formula for the slope \( m \) is:

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

Substituting in the coordinates of the points:

- \( (x_1, y_1) = (0, 1) \)
- \( (x_2, y_2) = (8, 0) \)

\[
m = \frac{0 - 1}{8 - 0} = \frac{-1}{8}
\]

Now that we have the slope, we can use one of the points to find the y-intercept \( b \). We'll use the point \( (0, 1) \), which directly gives us the y-intercept:

\[
b = 1
\]

Now we can write the equation of the line in slope-intercept form:

\[
y = -\frac{1}{8}x + 1
\]

Thus, the equation of the line is:

\[
y = -\frac{1}{8}x + 1
\]