Question

Use slope-intercept form, y = mx + b to find the equation of the line that passes through the points (−6, 1) and (3, 4).
y = –3x + 5
y = 3x – 5
y = one-third x + 3
y = negative one-third x + 5

Answer 1

To find the equation of the line that passes through the points (−6, 1) and (3, 4), we will start by determining the slope (m) using the formula:

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

For the points (−6, 1) and (3, 4):
- \( (x_1, y_1) = (-6, 1) \)
- \( (x_2, y_2) = (3, 4) \)

Now, substituting the values into the formula for slope:

\[
m = \frac{4 - 1}{3 - (-6)} = \frac{3}{3 + 6} = \frac{3}{9} = \frac{1}{3}
\]

Now that we have the slope \( m = \frac{1}{3} \), we can use one of the points to find the y-intercept \( b \). We'll use the point (3, 4) and the slope-intercept form of the equation \( y = mx + b \).

Substituting \( m \) and the coordinates of the point into the equation:

\[
4 = \frac{1}{3}(3) + b
\]

This simplifies to:

\[
4 = 1 + b
\]

Now, solving for \( b \):

\[
b = 4 - 1 = 3
\]

Thus, the equation of the line is:

\[
y = \frac{1}{3}x + 3
\]

Among the options you provided, the equation is equivalent to:

**\( y = \frac{1}{3}x + 3 \)**

So, the correct answer is:

**y = one-third x + 3.**