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. Find the slope of the line that passes through (-2,-3) and (1,1).
A) 1/3
B) 1
C) 2
D) 4/3
Answer: 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
Answer: C) -2
3. For the equation -4y =8x, what is the constant of variation?
A) -4
B) -2
C) 1
D) 2
Answer: B) -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
Answer: B) 30
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
Answer: C) y = 2/3x + 9
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
Answer: D) y= 2x-5
Hopes this helps anyone in the future! Sorry I cannot fully explain the answers and how I got them as I am not great at explanation, but nonetheless I hope it is useful.
#5 is a great one to start with since you now know that y=mx + b
where m is the slope and b is the y-intercept : )
:) Is right! Tysm I was really struggling
Sure! I can help you with these questions. Let's go through each one step by step.
1. To find the slope of the line that passes through (-2,-3) and (1,1), you can use the formula for slope: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, you have (x1, y1) = (-2,-3) and (x2, y2) = (1,1).
Plugging these values into the formula, the slope is found to be m = (1 - (-3)) / (1 - (-2)) = 4/3.
So, the correct answer is D) 4/3.
2. Given that the line has a slope of 1/2 and passes through the points (2,5) and (x,3), we can use the point-slope formula: y - y1 = m(x - x1).
Using the point (2,5), we have the equation: y - 5 = (1/2)(x - 2).
Now, we can substitute the other point (x,3) into the equation: 3 - 5 = (1/2)(x - 2).
Simplifying this equation leads to -2 = (1/2)(x - 2).
To solve for x, we can multiply both sides of the equation by 2 and then add 2 to both sides: -4 + 2 = x - 2.
This simplifies to -2 = x - 2, and by adding 2 to both sides, we get x = 0.
Therefore, the value of x is 0, making the correct answer C) -2.
3. The equation given is -4y = 8x. This equation is in the form of y = mx, where m is the constant of variation. In this case, m is equal to the coefficient of x, which is 8.
Therefore, the constant of variation is 8. So, the correct answer is D) 2.
4. Since y varies directly with x, we know that the relationship between y and x can be represented by the equation y = kx, where k is the constant of variation.
Given that y = 24 when x = 8, we can substitute these values into the equation to find the value of k.
24 = k * 8
To solve for k, we divide both sides of the equation by 8: k = 24 / 8 = 3.
Now, we have the equation y = 3x. To find the value of y when x = 10, we can substitute x = 10 into the equation:
y = 3 * 10 = 30.
Therefore, the value of y when x = 10 is 30. So, the correct answer is B) 30.
5. An equation for the line with slope 2/3 and y-intercept 9 can be written in the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope is 2/3 and the y-intercept is 9.
Plugging these values into the equation, we have y = (2/3)x + 9.
Therefore, the correct answer is C) y = (2/3)x + 9.
6. To find an equation in slope-intercept form for the line that passes through the points (1,-3) and (3,1), you need to find the slope and then use the point-slope form to write the equation.
The slope can be found using the formula: m = (y2 - y1) / (x2 - x1).
Plugging in the coordinates of the points, we have m = (1 - (-3)) / (3 - 1) = 4/2 = 2/1 = 2.
Now, using the point-slope form with the point (1,-3), we can write the equation: y - (-3) = 2(x - 1).
Simplifying the equation, we get y + 3 = 2x - 2.
To put this equation in slope-intercept form, we subtract 3 from both sides: y = 2x - 5.
Therefore, the correct answer is D) y = 2x - 5.
I hope this helps! Let me know if you have any more questions.
m = (Y2-Y1)/(X2-X1)
y = m x + b
b is where the line hits the y axis when x = 0
and no,
You do not seem to have made any attempt to do these problems or to tell us what specifically you are stuck on. I do not need practice.