1. Find the slope of a line that passes through (-2 -3) and (1 1).
a. 1/3
b. 1
c. 2
d. 4/2
2. For the equation -4y=8x, what is the constant of variation?
a. -4
b. -2
c. 1
d. 2
3. What is an equation in slope-intercept form for the line that passes through the points (1,-3) and (3,1)?
a. y=3x+1
b. y=x-3
c. y=2x+5
d. y=2x-5
I think B is -2
C is Y=2x-5
I think A is 1/3
Ok thanks Shalee :)
The first one was 4/3 but the other two were right thanks so much :)
oh :o
but yw
I just noticed I wrote 4/2 instead of 4/3 oops
1. slope = (1+3)/(1+2) = 4/3 , which is not in your list
2. -4y = 8x
y = -2x , so constant of variation is -2
3. d)
1. To find the slope of a line, you can use the formula: slope = (change in y-coordinates) / (change in x-coordinates). Let's call the first point (-2, -3) and the second point (1, 1).
The change in y-coordinates is (1 - (-3)) = 4.
The change in x-coordinates is (1 - (-2)) = 3.
So, the slope of the line passing through these two points is 4/3.
Therefore, the answer is not provided in the options. The correct slope is 4/3.
2. The equation -4y = 8x can be rewritten as y = (-8/4)x.
In the equation y = mx, where m represents the constant of variation, we can see that -8/4 is the value of m.
So, the constant of variation for this equation is -8/4, which simplifies to -2.
Therefore, the answer is b. -2.
3. To find the slope-intercept form of a line, we need the slope (m) and the y-intercept (b).
Using the formula for slope, we can calculate the slope (m) as follows:
m = (change in y-coordinates) / (change in x-coordinates)
m = (1 - (-3)) / (3 - 1)
m = 4 / 2
m = 2
Now, we have the slope (m) as 2.
Next, we can substitute the slope (2) and the coordinates of one of the given points, for example, (1, -3), into the slope-intercept form of a line (y = mx + b).
Using the point (1, -3):
-3 = 2(1) + b
Simplifying the equation:
-3 = 2 + b
To solve for b, we need to isolate it. Subtract 2 from both sides:
b = -3 - 2
b = -5
Therefore, the equation in slope-intercept form for the line passing through the points (1, -3) and (3, 1) is y = 2x - 5.
Therefore, the answer is d. y = 2x - 5.