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 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 (upward or downward).

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented as (0, 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).

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 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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What does it mean if the slope of a line is zero?

Back

If the slope of a line is zero, it means the line is horizontal and there is no change in y as x changes.

Tags

CCSS.8.EE.B.5

Front

What does it mean if the slope of a line is undefined?

Back

If the slope of a line is undefined, it means the line is vertical and there is no change in x as y changes.

Tags

CCSS.8.EE.B.5

Front

Write the equation for a line with a slope of 3 and a y-intercept of -2.

Back

The equation is y = 3x - 2.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you interpret the equation y = -2x + 20 in a real-world context?

Back

This equation represents a situation where for every minute (x), 2 gallons are drained from a tank that starts with 20 gallons.