More Solutions to Linear Equations

Lesson 13

Let’s find solutions to more linear equations!

Today’s Goal

• I can find solutions �(x, y) to linear equations given either the x- or the y-value to start from.

Coordinate Pairs

Warm Up

For each equation choose a value for x and then solve to find the corresponding y value that makes that equation true.

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(Let’s not use x=0…)

True or False:

Solutions in the Coordinate Plane

Activity 1

• MLR3: Clarify, Critique, Correct

For each statement, decide if it is true or false.

Begin working on your own.

Discuss �answers as a team.

If you disagree, work

together to come to an agreement!

1. (4,0) is a solution for line m.

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2. The coordinates of the point G

make both the equation for line

m and the equation for line n true.

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3. x = 0 is a solution of the equation

for line n.

false

true

false

4. (2,0) makes both the equation for

line m and the equation for line n

true.

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5. There is no solution for the

equation for line l that has y = 0.

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6. The coordinates of point H are

solutions to the equation for line l.

false

false

true

7. There are exactly two solutions of

the equation for line l.

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8. There is a point whose coordinates

make the equations of all three

lines true.

false

false

Big ideas:

• A solution of an equation in two variables is an ordered pair of numbers.
• Solutions of an equation lie on the graph of an equation.

I’ll Take an X, Please!

Activity 2

• MLR8: Discussion Supports

y = 5x – 11

One partner has 6 cards labeled A through F, and the other has 6 cards labeled a through F. In each pair of cards (A, a), there is an equation and a coordinate pair (x, y).

• The partner with the equation asks the partner with a solution for either the x or the y and explain why they chose that coordinate.
• The partner with the equation uses this value to find the other value, explaining the steps as they go.
• The partner with the coordinate pair then tells their partner if they’re correct or not. If incorrect, partners should look through the steps to find and correct error.
• Keep playing until you have finished cards A through F.

How did you decide whether you wanted the value of x or y?

Which equations represent proportional relationships?

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How do you know?

Which equations do not represent proportional relationships?

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How do you know?

Once you have identified one solution to your equation, what are some ways you could find others?

Note:

All of the equations in this activity are linear.

Linear equations are given in many forms, not just y=mx+b or Ax+By=C.

Are you ready for more?

Consider the equation ax + by = c, where a, b, and c are positive numbers.

1. Find the coordinates of the x- and y-intercepts of the graph of the equation.
2. Find the slope of the graph.

What are different ways to find a solution to the linear equation

3y + x = 12?

• substitute in a value for a variable and solve
• graph the equation and find points on the line
• rearrange the equation so that one variable is written in terms of the other variable

How do you know when you have found a solution to the equation

3y + x = 12?

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The coordinates of the point will make the statement true!

What are some easy values to substitute into the equation�3y + x = 12?

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Zero!

How can you find the slope of the line 3y + x = 12?

Graph it!

The slope is negative when y=-⅓x + 4.

Today’s Goal

• I can find solutions �(x, y) to linear equations given either the x- or the y-value to start from.

Intercepted

Cool Down