Question

Which statement best described the graph of the two equationsx + 4y = 83x + 12y = 2The lines are parallelThe lines are the sameThe lines intersect in only one point.The lines intersect in more than one point, but are not the same

Answer 1

The lines are parallel

Step-by-step explanation:

Given the following equations

x + 4y = 8

3x + 12y = 2

Step 1: convert the equations into a slope - intercept equation

y = mx + b

where m = slope and b = intercept

4y = -x + 8

Divide through by 4

y = -1/4x + 2

Therefore, m = - 1/4 in the above equation

For equation 2

3x + 12y = 2

12y = -3x + 2

Divide through by 12

y = -3x/12 + 2/12

y = -1/4x + 1/6

Therefore, m2 = -1/4

Since the two equations has the same slope, therefore, the lines are parallel