Solving Linear Equations in One Variable

Linear Equations in One Variable Class 8th

Linear equations in one variable are equations that can be written in the form y = mx + c, where m and c are constants, and x is the variable. These equations are called linear because the graph of a linear equation is a straight line. In this article, we will discuss how to solve linear equations and word problems involving linear equations.

Solving Linear Equations

To solve linear equations, follow these steps:

1. Write the equation in slope-intercept form: The slope-intercept form of a line is y = mx + c, where m is the slope and c is the y-intercept. If the equation is not already in slope-intercept form, you will need to rearrange it to get it into that form.

2. Identify the slope (m) and y-intercept (c): The slope is the coefficient of the variable (x), and the y-intercept is the constant term.

3. Use the slope and y-intercept to find the value of the variable (x): If you know one point on the line, you can use the point-slope form of a line to find the value of x. If you don't know any points, you can use the slope and y-intercept to find the equation of the line and then use the equation to find the value of x.

For example, let's solve the equation 3x + 2 = 0:

1. Write the equation in slope-intercept form: 3x + 2 = 0 becomes 3x = -2.
2. Identify the slope and y-intercept: The slope is 3, and the y-intercept is -2.
3. Use the slope and y-intercept to find the value of x: To find the value of x, we can rearrange the equation to get x = -2/3.

Word Problems Involving Linear Equations

Word problems involving linear equations are problems that can be modeled using a linear equation. These problems can be solved using the same steps as for linear equations. However, you may need to translate the problem into an equation before you can solve it.

For example, let's solve the following problem: A basketball player makes 80% of his free throws. If he attempts 10 free throws, how many will he make?

1. Write the equation: Let x be the number of free throws the player makes. The equation is 0.8x = 10.
2. Solve the equation for x: Divide both sides by 0.8 to get x = 12.5. Since the number of free throws must be a whole number, we round down to 12 free throws.

In conclusion, solving linear equations in one variable and word problems involving linear equations can be done using the same steps. First, write the equation in slope-intercept form, identify the slope and y-intercept, and then use the slope and y-intercept to find the value of the variable (x) or translate the problem into an equation and solve it.