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? (1 point)
–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
and you thinking is?
To find the slope of a line that passes through two points, you can use the formula:
m = (y2 - y1) / (x2 - x1)
For the given points (-2, -3) and (1, 1), you can substitute the values into the formula:
m = (1 - (-3)) / (1 - (-2))
= 4 / 3
Therefore, the slope of the line that passes through (-2, -3) and (1, 1) is the fraction four thirds.
For the equation –4y = 8x, the constant of variation can be found by rearranging the equation to the form y = kx, where k represents the constant of variation. Divide both sides of the equation by -4 to isolate y:
y = (-8/4)x
y = -2x
From this equation, we can see that the constant of variation is -2.
For the given scenario where y varies directly with x and y = 24 when x = 8, you can use the formula for direct variation:
y = kx
Substitute the given values into the equation:
24 = k * 8
Divide both sides of the equation by 8 to solve for k:
k = 24 / 8
= 3
Therefore, the value of y when x = 10 can be found by substituting the value of x into the equation:
y = k * x
y = 3 * 10
= 30
Hence, the value of y when x = 10 is 30.