1. 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
2. What is an equation in slope-intercept form for the line that passes through the points (1, –3) and (3, 1)?
A. y = 3x + 1
B. y = x – 3
C. y = 2x + 5
D. y = 2x – 5**
1. yes, y = 3 x so y = 30 when x = 10
2. slope = m = (1+3)/(3-1) = 2
so
y = 2 x + b
put a point in
1 = 2*3 + b
b = -5
so
y = 2 x - 5 agree
Thanks for the help
1. To determine the value of y when x = 10 in a direct variation equation, we need to find the constant of variation (k) first. The equation for direct variation is y = kx.
Given that y = 24 when x = 8, we can substitute these values into the equation: 24 = k(8).
To solve for k, we divide both sides of the equation by 8: k = 24/8 = 3.
Now, we can use the equation y = kx with the value of k we found: y = 3x.
Finally, substitute x = 10 into the equation: y = 3(10) = 30.
Therefore, the value of y when x = 10 is 30.
The correct answer is B. 30.
2. To write an equation in slope-intercept form (y = mx + b) for a line passing through two given points (x₁, y₁) and (x₂, y₂), we need to find the slope (m) and the y-intercept (b).
Using the formula for slope (m) between two points: m = (y₂ - y₁) / (x₂ - x₁),
we substitute the coordinates (1, -3) and (3, 1): m = (1 - (-3)) / (3 - 1) = 4 / 2 = 2.
Next, we choose one of the given points (1, -3) and substitute it for x and y in the equation y = mx + b: -3 = 2(1) + b.
To solve for b, we simplify the equation: -3 = 2 + b.
By subtracting 2 from both sides, we find b = -5.
Now, we can write the equation y = mx + b using the values of m and b: y = 2x - 5.
Therefore, the equation in slope-intercept form for the line passing through the points (1, -3) and (3, 1) is D. y = 2x - 5.
The correct answer is D. y = 2x - 5.
1. To solve this problem, we are given that y varies directly with x. This means that the relationship between y and x can be represented by the equation y = kx, where k is the constant of variation.
We are also given that y = 24 when x = 8. We can use this information to find the value of k.
Substituting the given values into the equation, we have:
24 = k * 8
To find the value of k, we divide both sides of the equation by 8:
k = 24 / 8
k = 3
Now that we have the value of k, we can find the value of y when x = 10 by substituting these values into the equation:
y = 3 * 10
y = 30
Therefore, the value of y when x = 10 is 30. Hence, the correct answer is B. 30.
2. To find the equation of a line that passes through two given points, we need to first calculate the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the given points are (1, -3) and (3, 1). We can use these coordinates to calculate the slope:
m = (1 - (-3)) / (3 - 1)
m = 4 / 2
m = 2
Next, we need to use the slope-intercept form of a linear equation, which is:
y = mx + b,
where m is the slope and b is the y-intercept. To find the value of b, we substitute the coordinates of one of the given points (1, -3) into the equation:
-3 = 2(1) + b
-3 = 2 + b
To solve for b, we subtract 2 from both sides:
b = -5
Now that we have the slope (m = 2) and the y-intercept (b = -5), we can write the equation of the line in slope-intercept form:
y = 2x - 5.
Therefore, the correct answer is D. y = 2x - 5.