Mrs. K's Advanced Math Midterm

Front

What does it mean for two ratios to be proportional?

Back

Two ratios are proportional if they have the same value when simplified. For example, the ratios \( \frac{15}{2} \) and \( \frac{30}{4} \) are proportional because both simplify to \( 7.5 \).

Front

What is the formula for slope in a coordinate plane?

Back

The formula for slope (m) is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on a line.

Front

Solve for \( a \): \( 5 = 4a - 7 \)

Back

\( a = 3 \)

Front

What is a ratio?

Back

A ratio is a comparison of two quantities by division. It shows how many times one value contains or is contained within the other.

Front

What is the difference between a proportional relationship and a non-proportional relationship?

Back

In a proportional relationship, the ratio between two variables is constant. In a non-proportional relationship, the ratio changes.

Front

How do you determine if a set of ratios is proportional?

Back

To determine if a set of ratios is proportional, cross-multiply and check if the products are equal.

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

What does the y-intercept represent in a graph?

Back

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

Front

If the slope of a line is 2, what does this mean?

Back

A slope of 2 means that for every 1 unit increase in x, y increases by 2 units.

Front

What is the formula to find the y-coordinate of a point on a line given the slope and x-coordinate?

Back

Using the slope-intercept form, you can find the y-coordinate by substituting the x-coordinate into the equation \( y = mx + b \).