Slope Review

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1)

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It is often expressed as a quantity per one unit of another quantity.

Front

If a car travels 300 miles using 15 gallons of fuel, what is the unit rate in miles per gallon?

Back

20 miles per gallon.

Front

What does a dilation transformation (x, y) → (kx, ky) represent?

Back

It represents a scaling of the figure by a factor of k, where k is the scale factor.

Front

What is the scale factor in the transformation (x, y) → (3.5x, 3.5y)?

Back

The scale factor is 3.5.

Front

What is a slope triangle?

Back

A slope triangle is a right triangle formed by the rise and run of a line on a graph, used to visually represent the slope.

Front

How can you find the slope using slope triangles?

Back

By measuring the vertical rise and horizontal run of the triangle and calculating the ratio rise/run.

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, meaning the line rises from left to right.

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, meaning the line falls from left to right.