Linear Relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using m = (y2 - y1) / (x2 - x1). Then use the point-slope form y - y1 = m(x - x1) to write the equation.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities, expressed as y = kx. It represents the ratio of y to x.

Front

If a linear function has a slope of 2, what does this mean?

Back

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

Front

What is the formula to convert inches to millimeters?

Back

To convert inches to millimeters, multiply the number of inches by 25.4, since 1 inch is equal to 25.4 millimeters.

Front

How do you solve for y in the equation y = 3/2x + 6?

Back

To solve for y, substitute a value for x into the equation. For example, if x = 2, then y = 3/2(2) + 6 = 3 + 6 = 9.

Front

What is a ratio?

Back

A ratio is a comparison of two quantities, showing how many times one value contains or is contained within the other. It can be expressed in the form a:b.

Front

How do you find the number of raisins if there are 600 almonds in a 4:3 ratio?

Back

If the ratio of almonds to raisins is 4:3, then for every 4 almonds, there are 3 raisins. To find the number of raisins, set up the proportion: 600 almonds / 4 = x raisins / 3. Solving gives x = 450 raisins.