Answer:
Slope of PQ = 0
Slope of MN = infinity
PQ and MN are perpendicular to each other
Step-by-step explanation:
for any two points (x1, y1), (x2, y2)given in coordinate plane slope is given by
For any line if slope is zero it is parallel to X axis and perpendicular to Y axis
For any line if slope is infinity it is parallel to Y axis and perpendicular to X axis
Also we know X and Y are perpendicular to each other.
Since slope of PQ is zero it is parallel to X axis and perpendicular to Y axis
Since slope of MN is infinity it is parallel to Y axis and perpendicular to X axis.
Thus two lines PQ and MN are perpendicular to each other.
Answer:
Option B k > 0
Step-by-step explanation:
we know that
Observing the graph
The slope of the line is positive
The y-intercept is negative
we have
![3y-2x=k(5x-4)+6\\ \\3y=5kx-4k+6+2x\\ \\3y=[5k+2]x+(6-4k)\\ \\y=\frac{1}{3}[5k+2]x+(2-\frac{4}{3}k)](https://tex.z-dn.net/?f=3y-2x%3Dk%285x-4%29%2B6%5C%5C%20%5C%5C3y%3D5kx-4k%2B6%2B2x%5C%5C%20%5C%5C3y%3D%5B5k%2B2%5Dx%2B%286-4k%29%5C%5C%20%5C%5Cy%3D%5Cfrac%7B1%7D%7B3%7D%5B5k%2B2%5Dx%2B%282-%5Cfrac%7B4%7D%7B3%7Dk%29)
The slope of the line is equal to
![m=\frac{1}{3}[5k+2]](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B3%7D%5B5k%2B2%5D)
Remember that the slope must be positive
so
The value of k is greater than -2/5
Analyze the y-intercept
1.5 is greater than zero
so
the solution for k is the interval ------> (1.5,∞)
therefore
must be true
k > 0
4y ≥ 3x + 2
Plugging in the values in the options, then the required values are when x = 6 and y = 5, then
4(5) ≥ 3(6) + 2
20 ≥ 18 + 2
20 ≥ 20
Answer:
parallel
Step-by-step explanation:
find the slope of each line
Line 1 (5-2)/(-4-2) = 3/-6 =-1/2
Line 2 (-4--9)/(-6-4)= 5/-10 = -1/2
16 vegetables because 75-68=7 and 80-71=9 and 9+7=16
