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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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 goes up, negative slope goes down).

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept (b) 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 graph the equation y = x - 4?

Back

To graph y = x - 4, start at the y-intercept (0, -4) and use the slope of 1 to rise 1 unit up and run 1 unit to the right to find another point.

Front

What is the equation of a line that has a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you determine if a point (x, y) lies on the line represented by a linear equation?

Back

Substitute the x-value into the equation and see if the resulting y-value matches the y-value of the 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, meaning they will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

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

Tags

CCSS.8.EE.B.6

Front

How can you find the equation of a line given two points?

Back

Use the slope formula (m = (y2 - y1) / (x2 - x1)) to find the slope, then use the point-slope form (y - y1 = m(x - x1)) to write the equation.

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.