Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that models a straight line in a coordinate plane, typically expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

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 slope means the line rises, negative slope means it falls).

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert a point-slope equation to slope-intercept form?

Back

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y to isolate it on one side.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

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

Back

To find the y-intercept from a linear equation in slope-intercept form (y = mx + b), identify the value of b, which is the y-coordinate where the line crosses the y-axis.

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. For example, it can indicate the initial amount of money before any transactions.

Front

How do you determine the slope from two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean if a line has an undefined slope?

Back

A line with an undefined slope is vertical, meaning it goes straight up and down. This occurs when the x-coordinates of the points on the line are the same.

Front

What is the relationship between parallel lines and their slopes?

Back

Parallel lines have the same slope but different y-intercepts. They never intersect.