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 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 (positive or negative).

Tags

CCSS.8.EE.B.5

Front

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

Back

To find the y-intercept of a linear equation, set x = 0 and solve for y. The y-intercept is the point where the line crosses the y-axis.

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

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

Back

y = -2/3x + 2.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the significance of the y-intercept in a real-world context?

Back

The y-intercept often represents the starting value or initial condition in a real-world scenario, such as the initial cost before any additional charges.

Tags

CCSS.HSF-IF.C.7A

Front

How do you determine the slope from a linear equation in standard form?

Back

From the standard form Ax + By = C, the slope can be determined by rearranging the equation into slope-intercept form (y = mx + b) and identifying m.

Tags

CCSS.8.EE.B.5

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Tags

CCSS.8.EE.B.5

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Tags

CCSS.8.EE.B.5

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means the line is horizontal, indicating that y remains constant regardless of the value of x.

Tags

CCSS.8.EE.B.5