 # Point-Slope Form of a Line

We can also find the equation of a line when given the slope and any point (not the y-intercept), and there are two methods to do so. The following video will use a single example to show how to use both methods to find the equation of a line with a given slope and single point.

These are the two methods to finding the equation of a line when given a point and the slope:

1. Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. Use the m given in the problem, and the b that was just solved for, to create the equation y = mx + b.
2. Point-slope form = $${\text{y}} {-} {\text{y}}_1 = {\text{m}}({\text{x}}-{\text{x}}_1)$$, where $$({\text{x}}_1, {\text{y}}_1)$$ is the point given and m is the slope given. The 'x' and the 'y' stay as variables.

Practice Problems

1. Find the equation of the line that passes through the point (1, 4) and has a slope of 12.

2. Find the equation of the line that passes through the point (1, 4) and has a slope of 2.

3. Find the equation of the line that passes through the point (27, 4) and has a slope of $$\frac{-2}{9}$$.

4. Find the equation of the line that passes through the point $$(-11, 2)$$ and has a slope of $$\frac{-5}{11}$$.

5. Find the equation of the line that passes through the point (10, 6) and has a slope of $$\frac{1}{5}$$. What is the y-intercept of the line?

6. Find the equation of the line that passes through the point (3, 29) and has a slope of 6. What is the y-intercept of the line?

#### Solutions

1. $${\text{y}} = 12{\text{x}} - 8$$

2. $${\text{y}} = 2{\text{x}} + 2$$ (Written Solution)

3. $${\text{y}} =-\frac{2}{9}{\text{x}}+10$$

4. $${\text{y}}=-\frac{5}{11}{\text{x}}-3$$

5. $$\left ( 0,4 \right )$$ (Written Solution)

6. $$(0,11)$$