Solutions of Linear Equations Introduction

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes.

Front

What is the y-intercept (b) in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It is the value of y when x = 0.

Front

How do you find the value of y in the equation y = 8x - 3 when x = 5?

Back

Substitute x = 5 into the equation: y = 8(5) - 3 = 40 - 3 = 37.

Front

What are coordinates?

Back

Coordinates are a set of values that show an exact position on a graph, usually written as (x, y).

Front

How do you write the solution x = 8, y = 10 as an ordered pair?

Back

The solution can be written as the ordered pair (8, 10).

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to locate a point on a graph, written in the form (x, y).

Front

How can you check if a point is a solution to a linear equation?

Back

Substitute the x-value of the point into the equation and see if the resulting y-value matches the y-value of the point.

Front

What is the solution to the equation y = 30 - 5x when x = 2?

Back

Substituting x = 2 gives y = 30 - 5(2) = 30 - 10 = 20, so the solution is (2, 20).

Front

What does it mean for a point to be on the line of a linear equation?

Back

A point is on the line of a linear equation if its coordinates satisfy the equation.