If the equation of line A shown on the graph is given by `y=mx+b`, and the equation of line B is given by `y=k(mx+b)`, what is the value of k?

Options

A. `(1)/(6)`
B. `(2)/(9)`
C. `6`
D. `9`

Answer

B

Explanation

Difficult: Hard
Category: Heart of Algebra/ Linear Equations
Strategic Advice: The equation of line B is given as a multiple of line A, so start by finding the equation of each line using its slope and y-intercept. Then compare the equations.
Getting to the Answer: First, determine the equation of line A. Remember that slope is equal to rise over run, so count the change in y and the change in x from one point, on the line to the next. The slope is `(3)/(1)` or just 3. Next, find the y-intercept: 9. Now, find the equation of line B: The slope is `(2)/(3)`, and the y-intercept is 2. So, the equation are: LIne A: `y=3x+9` and Line B: `y=(2)/(3)x+2`. Notice that the numbers in the equation of line A are larger, so k must be a fraction, which means you can eliminate C and D. To choose between A and B, multiply the number by the equation of line A see if it matches the equation of line B. Because `(2)/(9)(3x+9)=(2)/(3)x+2`( the equation of line B), `k=(2)/(9)`. Therefore, (B) is correct.