Find the slope (rate of change) of a line that passes through (–2, –3) and (1, 1).
(1 point)
1/3
1
2
4/3
The slope of a line can be found using the formula:
slope = (change in y) / (change in x)
Given the points (-2, -3) and (1, 1), we can calculate the change in y and change in x:
Change in y = 1 - (-3) = 4
Change in x = 1 - (-2) = 3
Now we can plug these values into the formula to calculate the slope:
slope = (change in y) / (change in x) = 4 / 3
Therefore, the slope of the line is 4/3.
For the equation –4y = 8x, what is the constant of variation? (1 point)
–4 –2 1 2
To find the constant of variation, we need to rewrite the equation in slope-intercept form y = mx + b, where m is the constant of variation.
Given the equation -4y = 8x, we can rearrange it to solve for y:
y = (-1/4) * 8x
Simplifying further, we have:
y = -2x
Comparing this to the slope-intercept form y = mx + b, we can see that the coefficient of x (-2) is the constant of variation.
Therefore, the constant of variation for the equation -4y = 8x is -2.
Suppose y varies directly with x, and y = 24 when x = 8. What is the value of y when x = 10?
(1 point)
10 30 80 240
Since y varies directly with x, we can set up the proportion:
y1 / x1 = y2 / x2
Given y1 = 24 and x1 = 8, we can substitute these values into the equation:
24 / 8 = y2 / 10
Simplifying further:
3 = y2 / 10
To solve for y2, we can multiply both sides of the equation by 10:
3 * 10 = y2
Therefore, y2 = 30.
So, when x = 10, the value of y is 30.