Question

A line passes through the points (6,10)
and (18,6)
. What is the equation of the line in slope-intercept form?(1 point)
Responses

y=13x+6
y equals Start Fraction 1 over 3 End Fraction x plus 6

y=−13x+12
y equals negative Start Fraction 1 over 3 End Fraction x plus 12

y=−3x+12
y equals negative 3 x plus 12

y=3x+6

Answer 1

To find the equation of the line that passes through the points (6,10) and (18,6), we first need to determine the slope (m) of the line using the formula:

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

Substituting the coordinates of the given points:

\[
m = \frac{6 - 10}{18 - 6} = \frac{-4}{12} = -\frac{1}{3}
\]

Next, we can use the point-slope form of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

Using one of the points, let's use (6,10):

\[
y - 10 = -\frac{1}{3}(x - 6)
\]

Now, distribute the slope:

\[
y - 10 = -\frac{1}{3}x + 2
\]

Then, add 10 to both sides to convert to slope-intercept form (y = mx + b):

\[
y = -\frac{1}{3}x + 12
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = -\frac{1}{3}x + 12
\]

The correct response is:

**y equals negative Start Fraction 1 over 3 End Fraction x plus 12**