If the line passing through the points
(a, 1) and (−2, 8)
is parallel to the line passing through the points
(12, 5) and (a + 2, 1),
what is the value of a?
a =
the slopes must be the same, so
(8-1)/(-2-a) = (1-5)/(a+2-12)
-7/(a+2) = -4/(a-10)
7(a-10) = 4(a+2)
7a-70 = 4a+8
3a = 78
a = 26
Since the lines are parallel this means the slopes are the same.
You then use y2-y1 (slope formula)
_____
x2-x1
and plug in both sets of points, (cross multipy) getting you
7(a-10)=-4(-2-a)
7a-70=8+4a
7a-4a=8+70
3a=78
a=26
To determine the value of a, we need to find the equation of the two given lines and set their slopes equal to each other. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope of the first line passing through the points (a, 1) and (-2, 8). The slope (m1) can be calculated using the formula:
m1 = (y2 - y1) / (x2 - x1)
Taking the points (a, 1) and (-2, 8), we have:
m1 = (8 - 1) / (-2 - a)
Next, let's find the slope of the second line passing through the points (12, 5) and (a + 2, 1). The slope (m2) can be calculated using the same formula:
m2 = (y2 - y1) / (x2 - x1)
Using the points (12, 5) and (a + 2, 1), we have:
m2 = (1 - 5) / (a + 2 - 12)
Now that we have the two slopes (m1 and m2), we can set them equal to each other:
m1 = m2
(8 - 1) / (-2 - a) = (1 - 5) / (a + 2 - 12)
Simplifying this equation gives us:
7 / (-2 - a) = -4 / (a - 10)
To eliminate fractions, we can cross multiply:
7(a - 10) = -4(-2 - a)
Expanding and simplifying:
7a - 70 = 8 + 4a
Combine like terms:
7a - 4a = 8 + 70
3a = 78
Divide both sides by 3:
a = 26
Therefore, the value of a is 26.