Linear Equations: Multiple Representations

Linear Equations: Multiple Representations

Recall finding slope

• from a graph

• from a table

• from two points

• from an equation

Multiple Choice

Find the slope in simplest form.

• $-\frac{4}{3}$

• $\frac{4}{3}$

• $-\frac{3}{4}$

• $\frac{3}{4}$

Multiple Choice

Find the slope in simplest form.

• 2

• -2

• 1

• -1

Multiple Choice

Find the slope from the equation.

 $y=\frac{1}{2}x-4$  

•  $-4$  

•  $\frac{1}{2}$  

• I'm confused.

• What is slope again?

Multiple Choice

Find the slope that passes through the points (4, 6) and (6, -2).

• $\frac{1}{4}$

• $-\frac{1}{4}$

• 4

• -4

3 forms of the linear equation

• slope-intercept form

• point-slope form

• standard form

Multiple Choice

Which form is represented by the following equation.

 $2x+3y=6$  

• slope-intercept form

• Standard form

• point-slope form

Multiple Choice

Which form is represented by the following equation?

 $y=-\frac{2}{3}x+2$  

• slope-intercept form

• point-slope form

• standard form

Multiple Choice

Which form is represented by the following equation?

 $y-4\ =\ -2\left(x+3\right)$  

• slope-intercept form

• point-slope form

• standard form

Writing linear equations

When writing linear equations, it is easier to use slope-intercept form (y=mx+b). The information we are given determines how we get there.

Writing a linear equation given a graph:

• Find 2 points on the line, find the slope (m): RISE over the RUN,

• Locate the y-intercept (b), where the graph crosses the y-axis,

• Place them into the equation y=mx+b

Write a linear equation for the following table:

• pick two points from the table

• calculate the slope

• pick one point from the table

• plug in your slope and your point into the point-slope equation y-y₁=m(x-x₁) then simplify and reduce until the equation is in slope-intercept form (y=mx+b)

• If the y-intercept is included in the table, you can skip this step and just plug your slope and intercept into y=mx+b

Write a linear equation using points:

• First, find the slope using the formula.

   $m=\frac{y_2-y_1}{x_2-x_1}$  

• Next, pick one of those points  $\left(x_1,\ y_1\right)$  

• Plug the slope (m) and the point  $\left(x_1,\ y_1\right)$   into the point-slope equation  $y-y_1=m\left(x-x_1\right)$  

• Simplify and reduce until you have the equation in slope-intercept form  $\left(y=mx+b\right)$ 

Write a linear equation from context:

• Identify the initial value or starting amount (y-intercept) in the problem.

• Identify the slope (Rate of Change).

• Plug the slope and y-intercept into the equation (y=mx+b)

• Everything depends on the information given.

• Remember the methods you've learned.

Multiple Choice

Clare owns a mobile pet grooming company. She charges $20 to come to your home plus $30 per hour to groom your pet. Which equation models the amount she charges over time?

• $y=50x$

• $y=20x+30$

• $y=30x+20$

• $20x+30y=50$

Poll

I understand how to write linear equations given two points, a table, and a graph.

• Yes, I can write linear equations.

• No, I need more help.