Graphing Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed on a coordinate plane. 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 of a line represent?

Back

The slope of a line represents the rate of change of the y-coordinate with respect to the x-coordinate. It indicates how steep the line is and the direction it is going (positive or negative).

Tags

CCSS.8.EE.B.5

Front

How do you find the y-intercept of a linear equation?

Back

The y-intercept of a linear equation can be found by setting x = 0 in the equation and solving for y. The resulting value of y is the y-intercept.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is 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

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 in terms of x.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is zero.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line is slanting downwards from left to right.

Tags

CCSS.8.EE.B.5

Front

What is the formula for calculating the slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

How can you determine if two lines are parallel?

Back

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

Tags

CCSS.8.EE.B.6

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other. If one line has a slope of m, the other line's slope will be -1/m.

Tags

CCSS.HSG.CO.A.1