Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) 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 y-intercept (b) in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using m = (y2 - y1) / (x2 - x1). Then use the point-slope form y - y1 = m(x - x1) to find the equation.

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

What does it mean if a line is vertical?

Back

A vertical line has an undefined slope and can be represented by an equation of the form x = a, where 'a' is a constant. It means that for every value of y, x remains constant.

Front

What does it mean if a line is horizontal?

Back

A horizontal line has a slope of 0 and can be represented by an equation of the form y = b, where 'b' is a constant. It means that for every value of x, y remains constant.

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b). They will never intersect.

Front

How do you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means that if one line has a slope of m, the other line's slope will be -1/m.

Front

What is the equation of a line that passes through the point (2, 3) with a slope of 4?

Back

Using the point-slope form, the equation is y - 3 = 4(x - 2), which simplifies to y = 4x - 5.