Linear Review

Front

What are the x- and y-intercepts on a graph?

Back

The x-intercept is the point where the graph crosses the x-axis (y=0), and the y-intercept is the point where the graph crosses the y-axis (x=0). For example, for the line with intercepts (5,0) and (0,5), the x-intercept is (5,0) and the y-intercept is (0,5).

Front

How do you identify the x- and y-intercepts from a linear equation?

Back

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

Front

What is the slope of a line that is perpendicular to another line with a slope of 3/2?

Back

The slope of a line that is perpendicular to another is the negative reciprocal. Therefore, the slope would be -2/3.

Front

How do you solve for y in the equation -6x + 3y = 9?

Back

To solve for y, isolate y: 3y = 6x + 9, then y = 2x + 3.

Front

What is the equation of a line that is perpendicular to 3x + 12y = 1 and passes through the point (-2, 6)?

Back

First, find the slope of the given line (which is -1/4). The perpendicular slope is 4. Using point-slope form: y - 6 = 4(x + 2) leads to y = 4x + 14.

Front

What is the definition of 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 represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope = increasing, negative slope = decreasing).

Front

How can you determine if two lines are parallel?

Back

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

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 convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form y = mx + b, solve for y: By = -Ax + C, then y = (-A/B)x + (C/B).