Linear Equations

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 (positive or negative).

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 is a proportional relationship?

Back

A proportional relationship is one where the ratio of y to x is constant. In a graph, this relationship is represented by a straight line that passes through the origin (0,0).

Front

How do you determine if a graph represents a proportional relationship?

Back

A graph represents a proportional relationship if it is a straight line that passes through the origin (0,0).

Front

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

Back

Proportional relationships have a constant ratio and pass through the origin, while non-proportional relationships do not have a constant ratio and may not pass through the origin.

Front

Write the equation for a line with a slope of 1 and a y-intercept of 2.

Back

y = 1x + 2 or simply y = x + 2.

Front

What does it mean if the slope of a line is negative?

Back

If the slope of a line is negative, it means that as x increases, y decreases. The line slopes downwards from left to right.

Front

How can you find the slope from two points on a line?

Back

The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.