Linear Equations

Front

What does it mean when y varies directly as x?

Back

It means that y is proportional to x, which can be expressed as y = kx, where k is a constant.

Front

If y = -4 when x = 32, what is the constant of variation (k)?

Back

k = y/x = -4/32 = -1/8.

Front

If y varies directly as x, what is the value of y when x = 64?

Back

y = kx = (-1/8) * 64 = -8.

Front

What is the slope of a line?

Back

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

Front

What is the slope of the line represented by the equation y = -3x + 5?

Back

The slope is -3.

Front

How do you find the x-intercept of a linear equation?

Back

Set y = 0 and solve for x.

Front

Find the x-intercept of the equation 3x + 8y = 24.

Back

The x-intercept is (8, 0).

Front

What is the average rate of change?

Back

It is the change in the value of a quantity divided by the change in time.

Front

Calculate the average rate of change in population from 1900 to 1990 if the population increased from 100 million to 250 million.

Back

Average rate of change = (250 - 100) million / (1990 - 1900) years = 1.5 million people/year.

Front

What is the formula for the slope between two points (x1, y1) and (x2, y2)?

Back

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