Slope, Slope Intercept, Rate of Change Review

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

How do you interpret a slope of 15 in a real-world context?

Back

A slope of 15 means that for every unit increase in the x-variable, the y-variable increases by 15 units. For example, if it represents earnings, you earn $15 for each lawn mowed.

Front

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

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find 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 a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What is the average rate of change?

Back

The average rate of change between two points is the slope of the line connecting those points, calculated as (change in y) / (change in x).

Front

If a line has a slope of 4/3, what does this mean in terms of rise and run?

Back

A slope of 4/3 means that for every 3 units you move horizontally (run), you move up 4 units (rise).

Front

How do you graph a line given the equation y = -1/3x - 4?

Back

To graph the line, start at the y-intercept (0, -4) and use the slope of -1/3 to find another point by going down 1 unit and right 3 units.

Front

What is the significance of the y-intercept in a linear equation?

Back

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