(8) Fall S1 Final Exam Study Guide

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value of the variable satisfies the equation, indicating that the two sides of the equation are equivalent for all values.

Front

Solve the inequality: 6x + 10 > 5x - 12

Back

x > -22

Front

What is the rate of change in a linear relationship?

Back

The rate of change is the ratio of the change in the dependent variable to the change in the independent variable, often represented as 'rise over run'.

Front

Solve the inequality: 4(2a + 3) < 3(a - 1)

Back

a < -3

Front

What does it mean for a slope to be constant?

Back

A constant slope means that the rate of change between two variables remains the same throughout the entire relationship.

Front

What is the solution to the equation: 4(-x + 3) = 2(6 - 2x)?

Back

Infinite solutions

Front

Define a linear equation.

Back

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

Front

What is the significance of the slope in a graph?

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables; a positive slope means an increase, while a negative slope means a decrease.

Front

Solve for x: 2x + 3 = 7

Back

x = 2

Front

What is the difference between a linear and a non-linear equation?

Back

A linear equation produces a straight line when graphed, while a non-linear equation produces a curve.