Writing 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 find the slope between two points (x1, y1) and (x2, y2)?

Back

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

Tags

CCSS.8.EE.B.5

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 can you determine if a linear equation is in slope-intercept form?

Back

A linear equation is in slope-intercept form if it is written as y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b). They will never intersect.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means one slope is the negative reciprocal of the other.

Tags

CCSS.8.EE.B.6

Front

How do you write the equation of a line given a point and a slope?

Back

You can use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the equation of a line that passes through the point (2, 3) with a slope of 4?

Back

Using the point-slope form: y - 3 = 4(x - 2) simplifies to y = 4x - 5.