slope intercept form

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 find the slope of a line given its equation in standard form?

Back

To find the slope from an equation in standard form (Ax + By = C), rearrange the equation to slope-intercept form (y = mx + b) and identify the coefficient of x as the slope.

Front

What does the slope of a line represent in a real-world context?

Back

The slope represents the rate of change or the steepness of the line, indicating how much the dependent variable changes for a unit change in the independent variable.

Front

How can you determine 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 y-intercept of a line?

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 do you write an equation for a linear relationship from a word problem?

Back

Identify the variables, determine the slope and y-intercept from the context, and then use the slope-intercept form (y = mx + b) to write the equation.

Front

What is the significance of a flat fee in a linear equation?

Back

A flat fee represents the y-intercept in a linear equation, indicating the starting value before any variable changes are applied.

Front

How do you graph a linear equation in slope-intercept form?

Back

Start by plotting the y-intercept (b) on the y-axis, then use the slope (m) to determine the rise over run to plot additional points.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates a vertical line, meaning x remains constant while y changes.