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 A and B are not both zero.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Tags

CCSS.8.EE.B.5

Front

How do you find the slope from the equation of a line in standard form?

Back

To find the slope from the standard form Ax + By = C, rearrange the equation into slope-intercept form (y = mx + b) and identify the coefficient of x (m) as the slope.

Tags

CCSS.8.EE.B.5

Front

What is 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 convert an 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 by isolating it on one side of the equation.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the y-intercept of a linear equation?

Back

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

Front

How can you determine the y-intercept from a linear equation in slope-intercept form?

Back

In slope-intercept form (y = mx + b), the y-intercept is the constant term b.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients in a linear equation determine the slope and the y-intercept, which define the line's steepness and its position on the graph.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you write a linear equation from a word problem?

Back

To write a linear equation from a word problem, identify the variables, determine the relationship between them, and express it in the form y = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

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

Back

If the slope of a line is negative, it means that as the value of x increases, the value of y decreases, indicating a downward trend.

Tags

CCSS.8.EE.B.5