If y equals a plus 12 times x plus 3 and y equals 4ax are parallel what is the value of a?

Answer 1

y = (a + 12)(x + 3) (line 1)
y = 4ax (line 2)

Since the equation of the second line is in a slope-intercept form, write the equation of the first line in the slope-intercept form, y = mx + b, where m is the slope of the line.

y = (a + 12)(x + 3)
y = a(x + 3) + 12(x + 3)
y = ax + 3a + 12x + 36
y = ax + 12x + 3a + 36
y = (a + 12)x + 3a + 36, where the slope is a + 12

y = 4ax, where slope is 4a

Since the lines are parallel they must have the same slope. So that,

a + 12 = 4a
3a = 12
a = 4

Thus, when a = 4, the parallel lines have a slope of 16.