Graphing Linear Equations in All Forms

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation 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 represents the rate of change of y with respect to x, indicating how steep the line is.

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

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, and A should be non-negative.

Front

How can you convert from slope-intercept form to standard form?

Back

Rearrange the equation y = mx + b to the form Ax + By = C by moving all terms to one side.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you graph a linear equation in slope-intercept form?

Back

Start by plotting the y-intercept (0, b) and then use the slope (rise/run) to find another point.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

How can you determine if a point lies on a line given by an equation?

Back

Substitute the x-coordinate of the point into the equation and see if the resulting y-value matches the y-coordinate of the point.