Hey, can someone help me out with these questions?
1. Find the slope of the line that passes through (-2,-3) and (1,1).
A) 1/3
B) 1*
C) 2
D) 4/3
2. A line with slope = 1/2 passes through the points (2,5) and (x,3). What is the value of x?
A) -1*
B) 1
C) -2
D) 2
3. For the equation -4y =8x, what is the constant of variation?
A) -4
B) -2
C) 1
D) 2*
4. 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
5. What is an equation for the line with slope 2/3 and y-intercept 9?
A) y = 2/3x
B) y=9x
C) y = 2/3x + 9*
D) 6= 9x +2/3
6. 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
ms.sue?
Sure, I can help you with these questions. Let's go through each question one by one.
1. To find the slope of the line that passes through (-2, -3) and (1, 1), we can use the formula for slope:
Slope (m) = (y2 - y1) / (x2 - x1)
Plugging in the coordinates, we get:
m = (1 - (-3)) / (1 - (-2))
= 4 / 3
So the slope of the line is 4/3.
The correct answer is D) 4/3.
2. Given that the line passes through (2, 5) and (x, 3), with a slope of 1/2, we can use the slope-intercept form of a line to find the value of x.
Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Plugging in the values, we get:
5 = (1/2) * 2 + b
5 = 1 + b
b = 5 - 1
b = 4
So the equation of the line is y = (1/2) x + 4.
To find x when y = 3, we can substitute the values into the equation:
3 = (1/2) x + 4
(1/2) x = 3 - 4
(1/2) x = -1
x = -2
Therefore, the value of x is -2.
The correct answer is C) -2.
3. 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.
Start by dividing both sides of the equation by -4:
y = -2x
Comparing this equation with the slope-intercept form, we can see that the constant of variation is the coefficient of x, which is -2.
The correct answer is B) -2.
4. Since y varies directly with x, we can write the equation as y = kx, where k is the constant of variation.
We're given that y = 24 when x = 8, so we can substitute these values into the equation:
24 = k * 8
Solving for k, we get:
k = 24 / 8
= 3
Now that we know the value of k, we can find y when x = 10:
y = 3 * 10
= 30
Therefore, the value of y is 30 when x = 10.
The correct answer is B) 30.
5. The equation for a line with slope m and y-intercept b is given by the slope-intercept form: y = mx + b.
In this case, we are given a slope of 2/3 and a y-intercept of 9. Plugging these values into the equation, we get:
y = (2/3) x + 9
Therefore, the correct answer is C) y = (2/3) x + 9.
6. To find the equation of the line that passes through the points (1, -3) and (3, 1) in slope-intercept form, we first need to find the slope (m).
Slope (m) = (y2 - y1) / (x2 - x1)
Plugging in the coordinates, we get:
m = (1 - (-3)) / (3 - 1)
= 4 / 2
= 2
Now that we know the slope, we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
Using the first point (1, -3):
y - (-3) = 2(x - 1)
y + 3 = 2x - 2
Rearranging the equation to the slope-intercept form, we get:
y = 2x - 5
Therefore, the correct answer is C) y = 2x + 5.
I hope this helps! Let me know if you have any other questions.
1 nope
2 nope
3 nope
4 yes
5 yes
6 nope
Were you just guessing?
It would have helped if you had shown your work, that way I could have helped.