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*
1. no
2. yes
3. no
4. yes
5. yes
6. yes
Sure, I can help you with these questions!
1. To find the slope of the line passing through (-2,-3) and (1,1), we use the formula for slope:
slope = (change in y)/(change in x)
slope = (1 - (-3))/(1 - (-2))
slope = 4/3
So, the correct answer is D) 4/3.
2. We are given that the line has a slope of 1/2 and passes through the points (2,5) and (x,3).
Using the formula for slope:
slope = (change in y)/(change in x)
1/2 = (3 - 5)/(x - 2)
1/2 = (-2)/(x - 2)
Cross multiplying, we have:
1(x - 2) = -4
x - 2 = -4
x = -4 + 2
x = -2
So, the correct answer is C) -2.
3. The equation -4y = 8x can be rewritten in slope-intercept form (y = mx + b) by solving for y:
-4y = 8x
y = -8x/4
y = -2x
The constant of variation is the coefficient of x, which is -2.
So, the correct answer is B) -2.
4. Since y varies directly with x, we have the equation y = kx, where k is the constant of variation.
To find the value of k, we can use the given information y = 24 when x = 8:
24 = k * 8
k = 24/8
k = 3
Now, we can find the value of y when x = 10:
y = 3 * 10
y = 30
So, the correct answer is B) 30.
5. An equation for a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
We are given the slope as 2/3 and the y-intercept as 9.
So, the equation for the line is y = (2/3)x + 9.
Thus, the correct answer is C) y = (2/3)x + 9.
6. The slope of the line passing through (1,-3) and (3,1) can be found using the formula for slope:
slope = (change in y)/(change in x)
slope = (1 - (-3))/(3 - 1)
slope = 4/2
slope = 2/1
So, the slope of the line is 2.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line and m is the slope, we can choose one of the given points (1,-3) to write the equation:
y - (-3) = 2(x - 1)
y + 3 = 2(x - 1)
y + 3 = 2x - 2
y = 2x - 2 - 3
y = 2x - 5
So, the correct answer is D) y = 2x - 5.
I hope this helps! Let me know if you have any further questions.
Sure, I'd be happy to help you with these questions!
1. To find the slope of a line passing through two points, you can use the formula: slope = (y2 - y1) / (x2 - x1).
In this case, the coordinates of the two points are (-2, -3) and (1, 1). Plugging these values into the formula, we get:
slope = (1 - (-3)) / (1 - (-2))
= 4 / 3
So the slope of the line passing through these points is 4/3. Therefore, the correct answer is D) 4/3.
2. We are given that the slope of the line is 1/2, and it passes through the points (2, 5) and (x, 3).
Using the formula for slope, (y2 - y1) / (x2 - x1), we can plug in the given values to find the equation:
(3 - 5) / (x - 2) = 1/2
Simplifying this equation, we get:
-2 / (x - 2) = 1/2
To solve for x, we can cross multiply and solve for x:
-2 = (x - 2)(1/2)
-4 = x - 2
x = -2
Therefore, the value of x is -2. So, the correct answer is C) -2.
3. For the equation -4y = 8x, we can rearrange it into the form y = mx + b, where m is the constant of variation.
Dividing both sides of the equation by -4, we get:
y = -2x
We can see that the coefficient of x, -2, is the constant of variation. Therefore, the correct answer is B) -2.
4. The problem tells us that y varies directly with x. This means that the equation can be written as y = kx, where k is the constant of variation.
We're also given that when x = 8, y = 24. Substituting these values into the equation, we have:
24 = k * 8
Solving for k, we get:
k = 24 / 8
k = 3
Now that we know the constant of variation is 3, we can find the value of y when x = 10:
y = kx
y = 3 * 10
y = 30
Therefore, the value of y when x = 10 is 30. So, the correct answer is B) 30.
5. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
In this case, we're given that the slope is 2/3 and the y-intercept is 9. Plugging these values into the equation, we get:
y = (2/3)x + 9
Therefore, the equation for the line with slope 2/3 and y-intercept 9 is C) y = (2/3)x + 9.
6. To find the equation in slope-intercept form for the line passing through the points (1, -3) and (3, 1), we can use the slope formula.
The slope (m) is given by: m = (y2 - y1) / (x2 - x1).
Using the coordinates of the two points, we have:
m = (1 - (-3)) / (3 - 1)
= 4 / 2
= 2
Now, we can use the formula y = mx + b and the point (1, -3) to calculate the y-intercept (b).
-3 = 2(1) + b
-3 = 2 + b
b = -5
Finally, substituting the values of m and b into the equation, we get:
y = 2x - 5
Therefore, the correct answer is D) y = 2x - 5.