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.

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.

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.

Front

Convert the equation 2y - 4x = 8 into slope-intercept form.

Back

y = 2x + 4.

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 ≥ 0.

Front

How do you convert 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 in terms of x.

Front

What does the term 'intercept' refer to in a linear equation?

Back

The intercept refers to the points where the line crosses the axes: the y-intercept is where x = 0, and the x-intercept is where y = 0.

Front

Write the linear equation for the word problem: 'A phone plan costs $50 per month plus $0.10 per text message.'

Back

y = 0.10x + 50.

Front

What is the x-intercept of the equation 5x + 2y = 10?

Back

The x-intercept is 2 (when y = 0, x = 2).