2.Find the slope of a line that passes through (–2, –3) and (1, 1).
The fraction one third.<
1
2
The fraction four thirds.
3.For the equation –4y = 8x, what is the constant of variation.
–4
–2
1 <
2
4.Suppose y varies directly with x, and y = 24 when x = 8. What is the value of y when x = 10?
10 <
30
80
240
To find the slope of a line, you can use the formula:
slope = (change in y) / (change in x)
1. Given the points (-2, -3) and (1, 1), we can calculate the change in y and change in x as follows:
change in y = 1 - (-3) = 4
change in x = 1 - (-2) = 3
Therefore, the slope of the line passing through these points is:
slope = (4) / (3) = 4/3
So, the correct answer is the fraction four thirds (4/3).
2. For the equation -4y = 8x, the constant of variation can be found by rearranging the equation to the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation can be rearranged as:
y = -2x
Since the slope of this equation is -2, the constant of variation is -2.
So, the correct answer is -2.
3. If y varies directly with x, it means that the ratio of y to x remains constant. This can be expressed as an equation:
y = kx
where k is the constant of variation.
Given that y = 24 when x = 8, we can substitute these values into the equation to solve for k:
24 = k * 8
k = 24/8 = 3
Now, we can find the value of y when x = 10 by substituting k = 3 and x = 10 into the equation:
y = 3 * 10 = 30
So, the value of y when x = 10 is 30.
Therefore, the correct answer is 30.