If y=(a+2)x+7 is parallel to y=3x-4, find the value of a.

Expert Answers
electreto05 eNotes educator| Certified Educator

Two lines are parallel if their slopes are equal.

The equation of a line is as follows:

y = mx + b

Where m is the value of the slope of the line and b is the intercept.

So that for each of the above lines, their slopes are:

y = (a+2)x + 7      →     m = (a+2)

y = 3x – 4             →     m = 3

Now we match the values of the slopes and isolate the value of a:

a + 2 = 3

a = 3 – 2

a = 1

General note:

If the lines are parallel, the slopes are equal:

m1 = m2

If the lines are perpendicular, the product of the slopes is equal to -1:

m1 . m2 = - 1   or   m1 = -1/m2

aishukul | Student

When two lines are parallel, their slopes are always equal. The formula in the problem is the slope-intercept formula. y=mx+b. M stands for the slope's value and b stands for the y-intercept.

If y=(a+2)x+7 is parallel to y=3x-4, find the value of a.

To find this, since the slopes of parallel lines are equal, that means the first formula's slope must be 3 since the second formula's slope is 3. Therefore, what value of a will give you three?

1+2=3. Therefore, a equals 1.

y=3x+7 and y=3x-4. The slopes are the same. Thus, the answer is 1.

shonasharma | Student

two lines are parallel if they have the same slope/gradient

the general equation for the straight line is:

y=mx + c

where m is always the gradient and c is your constant/y intercept

so, if the lines are parallel, the gradient should be same( the coefficient of x in your general equation should be same)

now, y=(a+2)x + 7

and y=3x - 4

so one equation has it clear that the coefficient of x is 3( that means 3 is the gradient). Hence, 3 must be the gradient of the other equation too.

so, we assume that a+2=3

what plus 2 will give us 3?

that's simple addition or subtraction we deal with and your answer is 1!