Graphing 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 (m) represent in a linear equation?

Back

The slope (m) 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 means the line rises, negative slope means it falls).

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How do you convert an equation to slope-intercept form?

Back

To convert an equation to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What is the slope-intercept form of the equation y = 2x + 3?

Back

The slope-intercept form is already y = 2x + 3, where the slope is 2 and the y-intercept is 3.

Front

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

Back

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

Front

What is the equation of a line with a slope of 3 that passes through the point (1, 2)?

Back

Using the point-slope form, the equation is y - 2 = 3(x - 1), which simplifies to y = 3x - 1.

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.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find the y-intercept, plot it on the graph, use the slope to find another point, and draw a straight line through the points.

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.