Linear Equations fall final math 8

Front

What is the formula to find the slope from two points?

Back

The slope (m) is calculated using the formula: m = (y₂ - y₁) / (x₂ - x₁).

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

How do you identify a linear equation from a table of values?

Back

If the change in y-values is constant for equal changes in x-values, the equation is linear.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

What is the meaning of the slope in a linear equation?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

Write a linear equation for a situation where a company charges a base fee plus a variable cost per unit. Example: $15 base fee and $4 per hour.

Back

y = 4x + 15, where y is the total cost and x is the number of hours.

Front

What is the difference between linear and nonlinear equations?

Back

Linear equations graph as straight lines, while nonlinear equations graph as curves.

Front

How can you determine if a graph represents a linear relationship?

Back

If the graph is a straight line, it represents a linear relationship.

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, y also increases.