What are linear equations and their graph?

A linear equation is a mathematical statement that shows a relationship between two variables, usually 𝑥 and 𝑦, and describes a straight line when graphed. The general form of a linear equation is:

y = mx + b

y: The value on the vertical axis (y-axis).

x: The value on the horizontal axis (x-axis).

m: The slope of the line, indicating how steep it is.

b: The y-intercept, where the line crosses the y-axis.

Imagine you have a job where you earn a fixed amount of money per hour worked. This can be represented by a linear equation.

Suppose:

You earn $15 per hour (this is the slope 𝑚).

You start with a bonus of $30 (this is the y-intercept 𝑏).

The linear equation representing your total earnings 𝑦 based on the number of hours worked 𝑥 would be:

y = 15x + 30

75
60
45
30
15
0
1
2
3
4
5
6
*
*

Quizzes:

1. A recipe calls for 2 cups of flour to make 8 cookies. If you want to make 16 cookies, how many cups of flour do you need? How many cups of flour do you need to make 16 cookies?

2. Driving at a speed of 50 miles per hour, you can cover 100 miles in 2 hours. How long will it take to cover 150 miles at the same speed?

3. A can of paint covers an area of 3 square meters. If you need to cover 15 square meters, how many cans of paint do you need? How many cans of paint do you need to cover 15 square meters?

4.A car can travel 30 miles on 1 gallon of gas. How far can it travel on 5 gallons of gas? How far can the car travel on 5 gallons of gas?

5. 5 apples cost $2.50. How much do 10 apples cost? How much do 10 apples cost?