Writing Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that models a straight line, typically 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, indicating how steep the line is and the direction it moves (positive or negative).

Front

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

Back

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

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

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Front

How do you write a linear equation given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), then rearrange to slope-intercept form if needed.

Front

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

Back

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

Front

How can you determine if a slope is positive, negative, or zero?

Back

A positive slope rises from left to right, a negative slope falls from left to right, and a zero slope is a horizontal line.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, cost per item, or growth rates in various contexts.

Front

How do 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 to isolate it on one side of the equation.