# Finding Where Lines Intersect Worksheets

Unless two lines are parallel, they will intersect, at a point, somewhere along the way. When lines intersect it means that they share the same ordered pair at least at a single point. This means that for one short blip in time, these linear equations shared the same conditions. When can use these intersections to learn a great deal more about the nature and possible trends that these linear equations are capable of. We can predict where the exact point where the two lines will intersect by using basic algebra or by actually graphing the line. To learn all three strategies, check the bottom of this page. These worksheets and lessons help students identify where two linear equations would intersect. Student will also understand the power and significance of that calculation towards a variety of problems.

### Aligned Standard: Grade 8 Expressions and Equations - 8.EE.C.8

- Lines Intersection Step-by-Step Lesson- Find the equation of the lines and then set them equal to each other.
- Guided Lesson - I throw some related word problems in this one. I see these types of questions on the tests all the time.
- Guided Lesson Explanation - These types of problems require a good bit of understanding. You might want to review this one with the kids.
- Independent Practice - Find out where all the lines intersect. They take this skill and use it later to find out timing on collisions in Science class around this time.
- Matching Worksheet - These are a really good mix of problems to start to work out with children.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Start with line intersections and then some tough critical thinking problems.

- Homework 1 - Find the point where the two lines intersect.
- Homework 2 - John has two brothers, Paul and Smith. One of them is twice as old as Paul. 90 is the total age of both of them. How old is Smith?
- Homework 3 - Plug the x value into either of the equations to determine the y value of the intersection.

### Practice Worksheets

This is one of the more difficult topics for students at this level.

- Practice 1 - Line A and B have the following points: Line A: (15, 12) and (-9, 3) Line B: (8, 4) and (-3, -6) Find the point where the two lines intersect.
- Practice 2 - Roy draws a triangle which has two complementary angles. He finds that one angle is 63˚ less than twice of the other angle. Identify the two angles.
- Practice 3 - Line A and B have the following points: Line A: (7, 4) and (-3, 5) Line B: (3, 6) and (-4, -4) Find the point where the two lines intersect.

### Math Skill Quizzes

I threw a review problem on each quiz.

- Quiz 1 - The cost of admission to a dance was $162 for 12 children and 3 adults. The admission was $122 for 8 children and 3 adults. How much was the admission for each child and adult?
- Quiz 2 - The cost of an apple is twice the cost of an orange. Write a linear equation in two variables to represent this statement.
- Quiz 3 - The total salary of Kate and Smith is $55,000. Kate gets $1500 more than Smith. What is the salary of Smith?

### How to Solve Equations That Have Two Unknown Variables?

After a student grasps the concept of solving an algebraic equation with one variable, they can move on to solving algebraic equations with two variables.

Consider the equations: 2x + 7 = 15, 2x = 15 - 7, x = 8/2 = 4

It is easy to find the value of x in this situation. When it comes to solving an equation with two variables, such as an equation where both x and y are unknown: 2x + 3y=15.

Note that it has infinite solutions, and no one can ask kids to solve such values using one standard strategy. There is always a set of equations where you can solve to find the values of two variables.

Consider a system of equations with two unknown variables like; Y = 2x + 4, y = 3x + 2.

By solving this system of equation, we are basically finding the point of intersection of the lines for each of these equations. Two methods can be used to calculate the values of the unknown, and these include the elimination method and the substitution method.

**Substitution Method** - The substitution method involves substituting one variable within an expression of containing the other variable.

2x + 4 = 3x + 2 Now by solving for x, we get;

x = 2 Substitute the value of x into any of these two equations to solve for y;

y = 2(2) + 4, y = 8. If we plug y into what we started with (either linear would do), we can easily solve for x.

**Elimination Method** - The elimination method requires adding or subtracting two equations to eliminate one variable to solve for the second variable and then substituting the calculating value in any of the equations to solve for the eliminated variable. We subtract the first equation from the second equation;

y = 3x+2, -y = -2x-4 We can eliminate y and solve for x; We get x = 2, and by substituting the value into any of these equations, we can solve for y and get y=8.

You can also graph both lines and wherever they intersect would be the ordered pair of interest. Graphing is not that reliable because sometimes they result in decimal values that make it difficult to be accurate with.