Question

A line passes through the point (2,-9) and has a slope of 3. And equation of the line is (y+9)/(x-2)=3 what is the equation of the line in slope intercept form

Answer 1

To convert the given equation of the line \(\frac{y + 9}{x - 2} = 3\) into slope-intercept form (y = mx + b), we can start by manipulating the equation.

1. **Multiply both sides by \(x - 2\)** to eliminate the fraction:

\[
y + 9 = 3(x - 2)
\]

2. **Distribute the 3 on the right side**:

\[
y + 9 = 3x - 6
\]

3. **Subtract 9 from both sides** to isolate \(y\):

\[
y = 3x - 6 - 9
\]

\[
y = 3x - 15
\]

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

\[
y = 3x - 15
\]

Here, the slope \(m\) is 3 and the y-intercept \(b\) is -15.