Question

Choose the correct linear equation given the slope and a point P.
m=5/6,P=(-6,-2)

Answer 1

To write the linear equation given the slope \( m = \frac{5}{6} \) and the point \( P(-6, -2) \), we can use the point-slope form of the equation of a line, which is:

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

where \( (x_1, y_1) \) is the point and \( m \) is the slope.

In this case, \( (x_1, y_1) = (-6, -2) \) and \( m = \frac{5}{6} \).

Plugging in these values, we have:

\[
y - (-2) = \frac{5}{6}(x - (-6))
\]

This simplifies to:

\[
y + 2 = \frac{5}{6}(x + 6)
\]

Now, to rearrange into slope-intercept form \( y = mx + b \), we distribute \( \frac{5}{6} \):

\[
y + 2 = \frac{5}{6}x + \frac{5}{6} \cdot 6
\]

Calculating \( \frac{5}{6} \cdot 6 = 5 \):

\[
y + 2 = \frac{5}{6}x + 5
\]

Next, subtract 2 from both sides:

\[
y = \frac{5}{6}x + 5 - 2
\]

Which simplifies to:

\[
y = \frac{5}{6}x + 3
\]

So the equation of the line in slope-intercept form is:

\[
\boxed{y = \frac{5}{6}x + 3}
\]