find the slope of the line that passes through (-2,1), (1,10).
A: 3
B: -3
C: 1/3
D: -1/3
Which equation represents a direct variation? What is the constant of variation?
A: 3y=2x+1;1
B: y=-5x-11;5
C: 4y=-12x;-3
D: y+7=2x-1;7
Suppose y varies directly with x, and y=12 when x=-3. what is the value of y when x=6?
A: -24
B: 2
C: -2
D: -4
the slope is (1-10)/(-2-1) = ?
direct variation is y = kx
so, which choice looks like that?
y = kx, so y/x = k, a constant value. So, you want y such that
y/6 = 12/-3
What is the equation of the line that passes through the points (0,4) and (3,-2)?
What is the equation of the line through (5,1) with a slope of -3?
review two-point and point-slope forms.
The 2-point is just like point-slope, but you have the extra step of finding the slope first.
The slope of the line through (0,4) and (3,-2) is (-2-4)/(3-0) = -2
So, now you have a point and a slope. The line is thus
y-4 = -2(x-0)
or
y+2 = -2(x-3)
Those both describe the same line.
Now use the point-slope form on the other line
To find the slope of the line that passes through (-2,1) and (1,10), we can use the formula:
slope = (y2 - y1) / (x2 - x1)
Let's substitute the given values into the formula:
slope = (10 - 1) / (1 - (-2))
= 9 / 3
= 3
Therefore, the slope of the line is 3. So, the correct answer is A: 3.
To determine which equation represents a direct variation and find the constant of variation, we need to look for an equation in the form y = kx, where k is the constant of variation.
Let's check each option:
A: 3y = 2x + 1
This equation is not in the form y = kx, so it does not represent direct variation.
B: y = -5x - 11
This equation is not in the form y = kx, so it does not represent direct variation.
C: 4y = -12x
This equation is in the form y = kx, where k = -12 / 4 = -3. So, it represents direct variation, and the constant of variation is -3.
D: y + 7 = 2x - 1
This equation is not in the form y = kx, so it does not represent direct variation.
Therefore, the correct answer is C: 4y = -12x; -3.
To find the value of y when x = 6, given that y varies directly with x and y = 12 when x = -3, we can use the formula:
y = kx, where k is the constant of variation.
First, let's find the value of k using the given information:
12 = k * (-3)
Dividing both sides by -3:
k = -4
Now we can substitute the value of k and the given value of x into the direct variation equation to find y:
y = (-4) * 6
= -24
Therefore, when x = 6, y = -24. So, the correct answer is A: -24.