Final Exam Review

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant.

Front

How can you determine if a table represents a proportional relationship?

Back

You can determine if a table represents a proportional relationship by checking if the ratios of corresponding values are equal.

Front

What happens to the side lengths of a triangle when it is transformed using the rule \( (x,y) \rightarrow (\frac{1}{4}x, \frac{1}{4}y) \)?

Back

The side lengths of the transformed triangle are \( \frac{1}{4} \) as long as the side lengths of the original triangle.

Front

What does the variable 'a' represent in the transformation rule \( (x,y) \rightarrow (ax, ay) \)?

Back

The variable 'a' represents the scale factor of the transformation, affecting the size of the image compared to the pre-image.

Front

If \( a < 1 \), what can be said about the size of the image compared to the pre-image?

Back

If \( a < 1 \), then the image is smaller than the pre-image.

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 from its equation?

Back

The slope of a line can be found from its equation in slope-intercept form \( y = mx + b \) by identifying the coefficient of \( x \), which is \( m \).

Front

What does the y-intercept represent in a graph?

Back

The y-intercept represents the point where the line crosses the y-axis, indicating the value of \( y \) when \( x = 0 \).

Front

What is a scale factor in transformations?

Back

A scale factor is a number that scales, or multiplies, the dimensions of a shape during a transformation.

Front

What is the effect of a scale factor greater than 1 on a shape?

Back

A scale factor greater than 1 enlarges the shape, making it larger than the original.