1. For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation. X: 16, 32, 48 Y: 4, 16, 36
2. Write an equation for the line that is parallel to the given line and passes through the given point. Y=5x+10; (2,14)
3. Write an equation for the line that is perpendicular to the given line and passes through the given point. Y-2=7/3 (x+5); (-4,9)
Aye, you did actually come back! I'm lucky that you're back so soon. I'll check your answers and see how you did.
Answer choices for 1:
Yes; y=2x
Yes; y=4x
Yes; y=8x
No
Answer choices for 2:
Y=1/5x+4
Y=1/5x-4
Y=5x-68
Y=5x+4
Answer choices for 3:
Y-9=-3/7 (x-4)
Y-9=3/7 (x-4)
Y-9=-3/7 (x+4)
Y-9=3/7 (x+4)
And what were your answers?
D, D, C?
Am I right?
correct on all three.
Ah, I was way too slow to answer, but that's fine. I agree with bob! :) (i was dealing with my own problem a couple problems below) ^^;
Thanks you!
1. To determine if y varies directly with x, we can check if the ratio of y to x is constant for all the values given. To do this, we divide each y-value by its corresponding x-value:
y/x: 4/16 = 1/4
16/32 = 1/2
36/48 = 3/4
Since the ratios are not all the same, y does not vary directly with x.
2. To find the equation for a line parallel to the given line, we know that parallel lines have the same slope. In the equation y = 5x + 10, the slope is 5. Therefore, any line parallel to this will also have a slope of 5.
We also have a point, (2, 14), that the parallel line must pass through. We can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
Plugging in the values, we get:
y - 14 = 5(x - 2)
Expanding and simplifying:
y - 14 = 5x - 10
y = 5x + 4
So, the equation for the line parallel to y = 5x + 10 and passing through the point (2, 14) is y = 5x + 4.
3. To find the equation for a line perpendicular to the given line, we know that perpendicular lines have slopes that are negative reciprocals. The given line has a slope of 7/3, so the perpendicular line will have a slope of -3/7 (the negative reciprocal).
We also have a point, (-4, 9), that the perpendicular line must pass through. Again, we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
Plugging in the values, we get:
y - 9 = (-3/7)(x - (-4))
Expanding and simplifying:
y - 9 = (-3/7)(x + 4)
y - 9 = (-3/7)x - 12/7
Adding 9 to both sides:
y = (-3/7)x - 12/7 + 9
y = (-3/7)x - 12/7 + 63/7
y = (-3/7)x + 51/7
So, the equation for the line perpendicular to y - 2 = (7/3)(x + 5) and passing through the point (-4, 9) is y = (-3/7)x + 51/7.