Changing Equations to Slope-Intercept Form

In class today, we focused on the important skill of converting equations into slope-intercept form. This form is super useful because it allows us to quickly identify the slope and y-intercept of a line. Remember, the slope-intercept form of a linear equation is:

$$y = mx + b$$

Where:

  • $y$ is the dependent variable
  • $x$ is the independent variable
  • $m$ represents the slope of the line
  • $b$ represents the y-intercept (the point where the line crosses the y-axis)

Why is Slope-Intercept Form Important?

Being able to convert to slope-intercept form makes graphing lines and understanding their behavior much easier. It gives you a clear picture of how the line is oriented on the coordinate plane.

How to Convert to Slope-Intercept Form

The main idea is to isolate $y$ on one side of the equation. This usually involves the following steps:

  1. Isolate the 'y' term: Use addition or subtraction to get the term with 'y' by itself on one side of the equation.
  2. Divide to solve for 'y': Divide both sides of the equation by the coefficient of 'y' to get 'y' completely by itself.

Let's look at some examples:

Example 1: Convert $2x + y = 5$ to slope-intercept form.

Subtract $2x$ from both sides:

$$2x + y - 2x = 5 - 2x$$ $$y = -2x + 5$$

Now it's in slope-intercept form! We can see that the slope, $m$, is $-2$ and the y-intercept, $b$, is $5$.

Example 2: Convert $3x + 2y = 8$ to slope-intercept form.

Subtract $3x$ from both sides:

$$3x + 2y - 3x = 8 - 3x$$ $$2y = -3x + 8$$

Divide both sides by 2:

$$\frac{2y}{2} = \frac{-3x + 8}{2}$$ $$y = -\frac{3}{2}x + 4$$

So, the slope is $-\frac{3}{2}$ and the y-intercept is $4$.

Example 3: Convert $2x - 3y = 12$ to slope-intercept form.

Subtract $2x$ from both sides:

$$2x - 3y - 2x = 12 - 2x$$ $$-3y = -2x + 12$$

Divide both sides by -3:

$$\frac{-3y}{-3} = \frac{-2x + 12}{-3}$$ $$y = \frac{2}{3}x - 4$$

In this case, the slope is $\frac{2}{3}$ and the y-intercept is $-4$.

Homework

Complete the assigned worksheet to practice these conversions. Remember to show your work step-by-step. Keep an eye on those negative signs!

Class Notes

  • Period 2: [Link to Period 2 Notes]
  • Period 6: [Link to Period 6 Notes]

Bonus Point: Write "game" to earn a bonus point today!