Linear Equations from Tables

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed on a coordinate plane. It can be 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 linear equation represent?

Back

The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How do you determine the slope from a table of values?

Back

To determine the slope from a table of values, calculate the change in y (Δy) divided by the change in x (Δx) between two points: slope (m) = (y2 - y1) / (x2 - x1).

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 can you convert a linear equation from slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms involving x and y on one side and the constant on the other.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts. This means they will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means they intersect at a right angle.

Front

How can 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 write the equation.

Front

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

Back

The coefficients in a linear equation indicate the relationship between the variables. The coefficient of x (slope) shows how much y changes for a unit change in x, while the constant term (y-intercept) shows the value of y when x is zero.