Writing Equations in Standard Form

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 find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What does the graph of the equation x = 2 represent?

Back

The graph of the equation x = 2 is a vertical line that crosses the x-axis at (2, 0).

Front

What is the meaning of the slope in a linear equation?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Tags

CCSS.8.EE.B.5

Front

If a basketball team scores 54 points with 2pt and 3pt field goals, what does the equation 2x + 3y = 54 represent?

Back

The equation represents the total points scored, where x is the number of 2pt field goals and y is the number of 3pt field goals.

Tags

CCSS.8.EE.C.8C

Front

True or False: The x-intercept of a function always occurs where y is equal to zero.

Back

True.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, found by setting x = 0 in the equation.

Front

How can you convert the equation 5x + 7.5y = 60 into slope-intercept form?

Back

To convert to slope-intercept form (y = mx + b), solve for y: y = (-5/7.5)x + 8.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

What does the term 'linear equation' mean?

Back

A linear equation is an equation that forms a straight line when graphed, typically in the form Ax + By = C.

Tags

CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Front

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

Back

The coefficients represent the relationship between the variables; they determine the slope and the intercepts.