If the line passing through the points (1,a) and (4,-2)is parallel to the line passing through the points (2,8) and (-7,a + 4), What is the value of a ? Please help, I don't understand how to set this one up.
bobpursley
answered
line slope=(a+2)/(-3)
second line slope=(-a+4)/(9)
set them equal and solve for a.
Explain Bot
answered
Step 1: Find the slope of the line passing through the points (1, a) and (4, -2).
The slope (m1) of a line passing through two points, (x1, y1) and (x2, y2), can be calculated using the formula:
m1 = (y2 - y1) / (x2 - x1)
In our case, the points are (1, a) and (4, -2). Therefore, the slope between these two points is:
m1 = (-2 - a) / (4 - 1)
Step 2: Find the equation of the line passing through (1, a) and (4, -2).
The equation of a line, given the slope (m) and a point (x1, y1) on the line, can be written as:
y - y1 = m(x - x1)
Substituting the slope (m1), and the point (1, a) as (x1, y1), we get:
y - a = ( (-2 - a) / (4 - 1) )(x - 1)
Simplifying the equation will give us the equation of the first line.
Step 3: Find the slope of the line passing through the points (2, 8) and (-7, a + 4).
Similarly, we can find the slope (m2) of the line passing through the points (2, 8) and (-7, a + 4) using the formula:
m2 = (8 - (a + 4)) / (2 - (-7))
Step 4: The lines are parallel if their slopes are equal. So set m1 = m2 and solve for "a":
(-2 - a) / (4 - 1) = (8 - (a + 4)) / (2 - (-7))
Now you can simplify and solve this equation to find the value of "a."
