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 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 slope means the line rises, negative slope means it falls).

Front

What is the y-intercept of 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 (x1, y1) and (x2, y2)?

Back

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

Front

What is point-slope form of a linear equation?

Back

Point-slope form is an equation of a line that passes through a given point (x1, y1) with a slope m, expressed as y - y1 = m(x - x1).

Front

Convert the equation y = 3x + 2 to slope-intercept form.

Back

The equation is already in slope-intercept form, where the slope (m) is 3 and the y-intercept (b) is 2.

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 the equation y = 2x - 1?

Back

To graph y = 2x - 1, start at the y-intercept (0, -1) and use the slope (2) to find another point: from (0, -1), go up 2 units and right 1 unit to (1, 1).

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.

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.