10 Questions
What is the first step in solving word problems involving linear equations?
Translate the problem into an equation
In the equation 0.8x = 10, what does 'x' represent?
Number of free throws made by the player
What is the value of x when solving the equation x = 2/3?
3/2
What is the significance of rounding down to 12 free throws in the given example?
To ensure the number of free throws is a whole number
What is the primary purpose of writing an equation in slopeintercept form when solving linear equations?
To identify the slope and yintercept
What is the slopeintercept form of a linear equation?
y = mx + c
In the equation y = 3x  5, what is the value of the slope?
3
If a linear equation is not in slopeintercept form, what must be done?
Rearrange it to get it into slopeintercept form
What does the yintercept represent in the context of a linear equation?
The value of y when x is 0
How would you find the value of x using the pointslope form of a line?
By knowing one point on the line and using it in the equation
Study Notes
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:

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

Identify the slope (m) and yintercept (c): The slope is the coefficient of the variable (x), and the yintercept is the constant term.

Use the slope and yintercept to find the value of the variable (x): If you know one point on the line, you can use the pointslope form of a line to find the value of x. If you don't know any points, you can use the slope and yintercept 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:
 Write the equation in slopeintercept form: 3x + 2 = 0 becomes 3x = 2.
 Identify the slope and yintercept: The slope is 3, and the yintercept is 2.
 Use the slope and yintercept 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?
 Write the equation: Let x be the number of free throws the player makes. The equation is 0.8x = 10.
 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 slopeintercept form, identify the slope and yintercept, and then use the slope and yintercept to find the value of the variable (x) or translate the problem into an equation and solve it.
Explore the process of solving linear equations in one variable and word problems involving linear equations. Learn to write equations in slopeintercept form, identify the slope and yintercept, and find the value of the variable (x) or translate word problems into equations.
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