Question

Which of the following is an equation of a line that is parallel to y = 4 x + 9 ? (Choose all correct equations.)

y = 2 x + 9
y = 4 x − 7
12 x − 3 y = 6
− 20 x + 5 y = 45

Answer 1

The second, third and fourth are parallel to the given equation

Explanation:

In order to determine if the slopes are the same, put all of the equations in slope-intercept form: y = mx + b. In order for lines in this form to be parallel, the m values of each have to be the exact same number, in our case, 4. Equation 2 has a 4 in the m position, just like the given, so that one is easy. Equation 2 is parallel.

Let's solve the third equation for y:

12x - 3y = 6 so

-3y = -12x + 6 and

y = 4x - 2. Equation 3 is parallel since there is a 4 in the m position.

Let's solve the fourth equation for y:

-20x + 5y = 45 so

5y = 20x + 45 and

y = 4x + 9. Equation 4 is also parallel since there is a 4 in the m position.