Question

The graph shows a line and two similar triangles.

On a coordinate plane, a line goes through (0, 3) and (6, 11). A small triangle has a rise of 4 and run of 3.

What is the equation of the line?
y = 3 x + 3
y = three-fourths x + 3
y = four-thirds x + 3
y = 4 x + 3

Answer 1

To find the equation of the line that passes through the points (0, 3) and (6, 11), we first need to determine the slope of the line using the formula for slope \( m \):

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

Substituting the given points (0, 3) and (6, 11) into the formula:

\[
m = \frac{11 - 3}{6 - 0} = \frac{8}{6} = \frac{4}{3}
\]

Now that we have the slope \( m = \frac{4}{3} \) and since we know the y-intercept from the point (0, 3), which is 3, we can use the slope-intercept form of the equation of a line, \( y = mx + b \):

\[
y = \frac{4}{3}x + 3
\]

So, the equation of the line is:

\[
y = \frac{4}{3}x + 3
\]

Therefore, the correct answer is:

**y = four-thirds x + 3**