Lesson 6: Writing Equations in Slope-Intercept Form

Property

We can easily determine the slope and intercept of a line if the equation was written in slope-intercept form, $y = mx + b$.
Now, we will do the reverse—we will start with the slope and y-intercept and use them to find the equation of the line.
To find an equation of a line with a given slope and y-intercept, substitute the slope ($m$) and the y-coordinate of the y-intercept ($b$) into the slope-intercept form, $y = mx + b$.

Examples

• Find the equation of a line with slope 4 and y-intercept $(0, 2)$. We substitute $m=4$ and $b=2$ into $y = mx + b$ to get the equation $y = 4x + 2$.

• Find the equation of a line with slope $-5$ and y-intercept $(0, -1)$. We substitute $m=-5$ and $b=-1$ into $y = mx + b$ to get the equation $y = -5x - 1$.

Property

To write an equation from a graph in slope-intercept form $y = mx + b$:

1. Identify the y-intercept $b$ where the line crosses the y-axis
2. Find the slope $m = \frac{\text{rise}}{\text{run}}$ using two clear points on the line
3. Substitute $m$ and $b$ into $y = mx + b$

Examples

Property

To write an equation in slope-intercept form, $y = mx + b$, given the y-intercept and another point:

1. Use the two points $(x_1, y_1)$ and $(x_2, y_2)$ to calculate the slope:
   $$m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$$
2. Identify the y-intercept, $b$, from the point $(0, b)$.
3. Substitute the values for $m$ and $b$ into the equation $y = mx + b$.

Examples