Find the slope of a line that passes through (-2,-3) and (1,1).
a. 1/3
b. 1
c. 2
d. 4/3
For the equation -4y=8x, what is the constant of variation?
a. -4
b. -2
c. 1
d. 2
Suppose y varies directly with x, and y=24 when x=8. What is the value of y when x=10
a. 10
b. 30
c. 80
d.240
How can I check your work if you did not supply any of your choices
To find the slope of a line that passes through two points, (-2, -3) and (1, 1), you can use the formula:
slope = (y2 - y1) / (x2 - x1)
Using the coordinates, we have:
x1 = -2
y1 = -3
x2 = 1
y2 = 1
Substituting the values into the formula, we get:
slope = (1 - (-3)) / (1 - (-2))
= (1 + 3) / (1 + 2)
= 4 / 3
Therefore, the slope of the line that passes through (-2, -3) and (1, 1) is 4/3.
So, for the first question, the correct answer is (d) 4/3.
For the equation -4y = 8x, in order to find the constant of variation, we need to rewrite it in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
To do that, we can divide both sides of the equation by -4:
-4y / -4 = 8x / -4
y = -2x
The constant of variation for this equation is the coefficient of x, which is -2.
So, for the second question, the correct answer is (b) -2.
For the third question, since y varies directly with x, we know that there is a constant k so that y = kx.
Given that y = 24 when x = 8, we can substitute these values into the equation to find k:
24 = k * 8
k = 24 / 8
k = 3
So, the equation becomes y = 3x.
Now, we can find the value of y when x = 10 by substituting x = 10 into the equation:
y = 3 * 10
y = 30
Therefore, for the third question, the correct answer is (b) 30.