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
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
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.
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!