Slope & Direct Variation

Front

What is slope in mathematics?

Back

Slope is a measure of the steepness of a line, calculated as the rise over run between two points on the line.

Front

What does it mean for two variables to vary directly?

Back

Two variables vary directly if they have a constant ratio, meaning as one variable increases, the other variable increases proportionally.

Front

What is the equation of direct variation?

Back

The equation of direct variation is y = kx, where k is the constant of variation.

Front

If y = 3x, what is the constant of variation?

Back

The constant of variation is 3.

Front

How do you determine if y varies directly with x from the equation y + 3 = 3x?

Back

Rearranging gives y = 3x - 3, which is not in the form y = kx, so y does not vary directly with x.

Front

What is the slope of the line represented by the equation y = 2x + 1?

Back

The slope is 2.

Front

If y = 15/7 x, does y vary directly with x?

Back

Yes, because it can be expressed in the form y = kx.

Front

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

Back

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

Front

Write the direct variation equation if y = 18 when x = 12.

Back

y = 3/2 x.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.