Writing Linear Equations

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 determine the slope from two points (x1, y1) and (x2, y2)?

Back

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

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

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

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y: y = (-A/B)x + (C/B).

Front

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

Back

The slope indicates the rate of change of y with respect to x; it shows how steep the line is and the direction it goes.

Front

How do you find the equation of a line given a point and the slope?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the formula for finding the equation of a line given two points?

Back

First, calculate the slope using m = (y2 - y1) / (x2 - x1). Then use the point-slope form to find the equation.

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph.

Front

How do you interpret the coefficients in a linear equation?

Back

The coefficient of x (slope) indicates the change in y for a one-unit change in x, while the constant term (y-intercept) indicates the value of y when x is zero.

Front

What is the relationship between parallel lines in terms of their slopes?

Back

Parallel lines have the same slope but different y-intercepts.