Question

A line has a slope of 8 and passes through the point (1,3). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

To find the equation of a line in slope-intercept form, we use the formula:

\[ y = mx + b \]

where:
- \( m \) is the slope of the line,
- \( b \) is the y-intercept.

We are given the slope \( m = 8 \) and a point on the line \( (1, 3) \). We can use this point to find the y-intercept \( b \).

1. Substitute the slope and the coordinates of the point into the equation:

\[ y = 8x + b \]

2. Substitute \( x = 1 \) and \( y = 3 \) into the equation:

\[ 3 = 8(1) + b \]

3. Simplify and solve for \( b \):

\[ 3 = 8 + b \]

\[ b = 3 - 8 \]

\[ b = -5 \]

Now that we have both \( m \) and \( b \), the equation of the line in slope-intercept form is:

\[ y = 8x - 5 \]

Thus, the equation of the line is:

\(\boxed{y = 8x - 5}\)