Slope All Representations Review

Front

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

Back

The slope-intercept form is 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 two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the value of y when x = 0; it is where the line crosses the y-axis.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

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

Front

What is the slope of a line that is vertical?

Back

The slope of a vertical line is undefined because the change in x is 0.

Front

How can you write the equation of a line given its slope and a point on the line?

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 calculating the total cost if a basket costs $3 and each pound of fruit costs $2.50?

Back

The total cost can be expressed as y = 2.50x + 3, where x is the number of pounds of fruit.

Front

How do you convert the equation y = 2x + 5 to slope-intercept form?

Back

The equation is already in slope-intercept form, where the slope is 2 and the y-intercept is 5.

Front

What is the equation of a line that passes through the points (1, 2) and (3, 4)?

Back

First, find the slope: m = (4 - 2) / (3 - 1) = 1. Then use point-slope form: y - 2 = 1(x - 1) or y = x + 1.