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).

Front

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

Back

The y-intercept of a linear equation is found by setting x = 0 in the equation and solving 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

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

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

Back

The y-intercept represents the starting value of a situation when the independent variable (x) is zero.

Front

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

Back

y = -2/3x + 2.

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.

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.

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 does not change as x changes.