For the equation –4y = 8x, what is the constant of variation?
(1 point)
–4
–2
1
2
The constant of variation is the coefficient of x in the equation. So for the equation -4y = 8x, the constant of variation is 8.
that is not a answer
Apologies for the confusion. The constant of variation is the ratio between the variables. In this equation, the variable y is multiplied by -4 and x is multiplied by 2 to create a proportional relationship. Therefore, the constant of variation is -4/2, which simplifies to -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
If y varies directly with x, we can write the equation in the form of y = kx, where k is the constant of variation.
To find the value of y when x = 10, we can use the given information that y = 24 when x = 8.
Using this information, we can set up a proportion:
y/x = y/x
24/8 = y/10
Simplifying this equation, we get:
3 = y/10
Multiplying both sides by 10, we get:
30 = y
Therefore, when x = 10, the value of y is 30.
What is an equation for the line with slope (rate of change) 2/3
and y-intercept 9?
(1 point)
y = 2/3x
y = 9x
y = 2/3x + 9
y = 9x +2/3
The equation for a line with slope (rate of change) 2/3 and y-intercept 9 is given by the slope-intercept form of a linear equation, which is y = mx + b. In this form, m represents the slope and b represents the y-intercept.
Therefore, the equation for the given line is:
y = (2/3)x + 9
What is an equation in slope-intercept form for the line that
passes through the points (1, –3) and (3, 1)?
(1 point)
y = 3x + 1
y = x – 3
y = 2x + 5
y = 2x – 5
To find the equation of a line in slope-intercept form (y = mx + b) given two points, we need to determine the slope (m) and the y-intercept (b).
Given the points (1, -3) and (3, 1), we can find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (1 - (-3)) / (3 - 1)
m = 4 / 2
m = 2
Now that we have the slope (m = 2), we can substitute it into the slope-intercept form:
y = mx + b
y = 2x + b
Next, we can use one of the points (1, -3) to find the value of b. Substitute the x and y values from the point into the equation:
-3 = 2(1) + b
-3 = 2 + b
b = -5
Finally, substitute the value of b (-5) back into the equation:
y = 2x - 5
Therefore, the equation in slope-intercept form for the line that passes through the points (1, -3) and (3, 1) is:
y = 2x - 5