Linear Equations Two Variables

Front

What is a linear equation in two variables?

Back

A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables.

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.EE.B.6

CCSS.8.F.A.3

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

Convert the equation 3y - 2x = 6 into slope-intercept form.

Back

y = (2/3)x + 2.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the slope of the line represented by the equation y = 4x - 5?

Back

The slope is 4.

Tags

CCSS.8.EE.B.5

Front

If a line has a slope of -3, what does this indicate about the line's direction?

Back

A slope of -3 indicates that the line descends from left to right.

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.

Front

How do you rearrange the equation 5y - 15 = 10x into slope-intercept form?

Back

Rearranging gives y = 2x + 3.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the significance of the coefficients in the equation y = mx + b?

Back

The coefficient m represents the slope of the line, and b represents the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3