Direct Variation & Writing Systems

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, expressed as y = kx, where k is a non-zero constant.

Front

If y varies directly with x and y = 12 when x = 4, what is the constant of variation (k)?

Back

k = 3 (since y = kx, 12 = k(4) => k = 12/4 = 3).

Front

How do you write an equation for direct variation?

Back

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

Front

What does it mean if two lines represented by a system of equations intersect?

Back

If two lines intersect, it means the system of equations has one unique solution.

Front

What is the formula to find the constant of variation in direct variation problems?

Back

The constant of variation (k) can be found using the formula k = y/x.

Front

If a person earns $15 per hour, how much will they earn in 10 hours?

Back

$150 (15 * 10 = 150).

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.

Front

How do you solve a system of equations graphically?

Back

To solve graphically, plot each equation on the same graph and identify the point(s) where they intersect.

Front

What does it mean if a system of equations has no solution?

Back

It means the lines are parallel and will never intersect.

Front

If y = 5x and x = 3, what is the value of y?

Back

y = 15 (5 * 3 = 15).