4.3 Review QZ

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 of a line represent?

Back

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

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the y-intercept in a linear equation?

Back

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

Front

What does it mean for a relationship to be proportional?

Back

A relationship is proportional if it can be represented by a linear equation of the form y = kx, where k is a constant. This means that as x increases, y increases at a constant rate.

Front

What is the difference between proportional and non-proportional relationships?

Back

Proportional relationships pass through the origin (0,0) and can be expressed as y = kx. Non-proportional relationships do not pass through the origin and can be expressed as y = mx + b, where b ≠ 0.

Front

What is the equation of a line with a slope of 4/3 and a y-intercept of 0?

Back

The equation is y = (4/3)x.

Front

How can you identify a linear relationship from a graph?

Back

A linear relationship can be identified from a graph if the points form a straight line.

Front

What is the formula for finding the y-value given an x-value in a linear equation?

Back

To find the y-value, substitute the x-value into the equation y = mx + b.

Front

What does the term 'rate of change' refer to in a linear function?

Back

The rate of change refers to how much y changes for a unit change in x, which is represented by the slope of the line.