Converting Between Linear Forms

Converting Between Linear Equation Forms

​Types of Linear Equations

Categorize

Options (12)

$$y=-\frac{1}{2}x+6$$  

$$y-5=\frac{2}{3}\left(x+2_{ }\right)$$  

$$2x-3y=12$$  

$$y=5x+14$$  

$$y+3=5\left(x-7\right)$$  

$$5x-7y=10$$  

$$y-11=-\frac{5}{8}\left(x-9\right)$$  

$$12x+y=2$$  

$$y=\frac{4}{7}x-3$$  

$$y=mx+b$$  

$$y-y_1=m\left(x-x_1\right)$$  

$$Ax+By=C$$  

Arrange the given linear equations, so they are in the column corresponding to their form.

Slope-Intercept Form

Point-Slope Form

Standard Form

​Example:

• Distribute m

• ​Add/Subtract y₁

​From Point-Slope Form

Converting to Slope-Intercept Form

• Add/subtract the x-term

• ​Divide by coefficient of y

​From Standard Form

Converting to Slope-Intercept Form

Example:

Multiple Choice

Rewrite the following linear equation in slope-intercept form.

$$y+3=-3\left(x-1\right)$$

• $$y=-3x+6$$

• $$y=-3x$$

• $$y=-3x-6$$

• $$y=-3x-4$$

Multiple Choice

Rewrite the following linear equation in slope-intercept form.

$$7x+3y=-12$$

• $$y=-7x-12$$

• $$y=-\frac{7}{3}x-12$$

• $$y=-\frac{7}{3}x-4$$

• $$y=\frac{7}{3}x+4$$

• $$y=7x+4$$

​Example:

• Distribute m

• Multiple by the common denominator of any fractions

• Add/subtract the x-term

• Add/Subtract y₁

​From Point-Slope Form

Converting to Standard Form

​Example:

• Multiple by the common denominator of any fractions

• Add/subtract the x-term (to get the variables on the same side)

• Optional: Multiply the equation by -1 so the A is positive

​From Slope-Intercept Form

Converting to Standard Form

Multiple Choice

Rewrite the following linear equations in standard form.

$$y+\frac{3}{4}=2\left(x-2\right)$$

• $$8x-4y=19$$

• $$-8x+4y=-13$$

• $$-6x+4y=-19$$

• $$6x-4y=11$$

Multiple Choice

Rewrite the following linear equations in standard form.

$$y=-\frac{1}{5}x-8$$

• $$5x+y=40$$

• $$x+y=-40$$

• $$x+5y=-8$$

• $$x+5y=-40$$