Writing 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

How do you find the slope from two points?

Back

The slope (m) can be calculated 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 slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3.

Front

How do you write the equation of a line given a slope and a y-intercept?

Back

You can write the equation in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the equation of a line with a slope of -1 and a y-intercept of 4?

Back

The equation is y = -1x + 4 or y = -x + 4.

Front

What does it mean if a line has a slope of 0?

Back

A slope of 0 means the line is horizontal and does not rise or fall as it moves along the x-axis.

Front

What does it mean if a line has an undefined slope?

Back

An undefined slope means the line is vertical, and it does not have a defined rise over run.

Front

How do you determine if a point lies on a line represented by an equation?

Back

To determine if a point (x, y) lies on the line, substitute the x-value into the equation and see if the resulting y-value matches the y-value of the point.