sorry I wrote problem wrong:
Which equation would you use to find out if the two lines in the graph are parallel:(a)(1,4) and (-1,1) (b) (3,3) and (-1,-1)
a. 4-1/-2-1 = 3-1/3-1
b. 4-1/-2-1 = 3-(-1)/3-1
c. 4-1/1-(-2)= 3-(-1)/3-(-1)
d. 1-(-2)/4-1 = 3-1/3-1
I'd use
(4-1)/(1+1) = (3+1)/(3+1)
Don't know why all the choices have a -2 in them, since none of the points contains a -2.
Because Bubbles wrote it wrong one of the points is supposed to be (-2,1). Hope that helps! :D
To determine if two lines are parallel, we need to compare the slopes of the lines.
The equation for the slope between two points (x₁, y₁) and (x₂, y₂) is given by:
slope = (y₂ - y₁) / (x₂ - x₁)
For the given points:
(a) (1,4) and (-1,1)
Using the slope formula, we have:
slope₁ = (1 - 4) / (-1 - 1) = -3 / -2 = 3/2
(b) (3,3) and (-1,-1)
Using the slope formula, we have:
slope₂ = (-1 - 3) / (-1 - 3) = -4 / -4 = 1
Now, we compare the slopes:
(a) slope₁ ≠ slope₂ (3/2 ≠ 1)
(b) slope₁ ≠ slope₂ (3/2 ≠ 1)
Since the slopes of both cases are not equal, the lines are not parallel.
Therefore, none of the options provided is the correct equation for determining if the two lines are parallel.
To determine whether two lines are parallel, you need to compare their slopes. In general, if two lines have the same slope, they are parallel.
To find the slope of a line, you can use the formula:
slope = (y2 - y1) / (x2 - x1)
Let's apply this formula to the given points and check which equation represents the correct slope for each pair.
(a) For points (1, 4) and (-1, 1):
Slope = (1 - 4) / (-1 - 1) = -3 / -2 = 3/2
(b) For points (3, 3) and (-1, -1):
Slope = (-1 - 3) / (-1 - 3) = -4 / -4 = 1
Now, compare the calculated slopes with the slopes in each equation:
a. (4 - 1) / (-2 - 1) = (3 - 1) / (3 - 1) -> Correctly calculates the slope for points (1, 4) and (-1, 1)
b. (4 - 1) / (-2 - 1) = (3 - (-1)) / (3 - 1) -> Incorrectly calculates the slope for points (3, 3) and (-1, -1)
c. (4 - 1) / (1 - (-2)) = (3 - (-1)) / (3 - (-1)) -> Incorrectly calculates the slope for points (3, 3) and (-1, -1)
d. (1 - (-2)) / (4 - 1) = (3 - 1) / (3 - 1) -> Incorrectly calculates the slope for points (3, 3) and (-1, -1)
From the above analysis, the correct equation to find out if the two lines in the graph are parallel is option (a):
4 - 1 / -2 - 1 = 3 - 1 / 3 - 1