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*
see your earlier post
Of course! I'll help you answer these questions step by step.
1. To find the slope of a line passing through two points, you can use the formula:
slope = (y2 - y1) / (x2 - x1)
Given the points (-2,-3) and (1,1), the slope would be:
slope = (1 - (-3)) / (1 - (-2))
slope = 4 / 3
Therefore, the correct answer would be A) 1/3.
2. Since you know the slope of the line is 1/2 and one of the points on the line is (2,5), you can use the point-slope form of a line:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Plugging in the values, you get:
y - 5 = (1/2)(x - 2)
Now, you need to rearrange the equation to find the value of x. Let's simplify:
2(y - 5) = x - 2
2y - 10 = x - 2
2y - x = 8
Since the point (x,3) lies on the line, you know that the equation 2y - x = 8 holds true. Plugging in y=3:
6 - x = 8
-x = 2
x = -2
Therefore, the correct answer is C) -2.
3. For the equation -4y = 8x, the constant of variation can be determined by isolating y:
Divide both sides of the equation by -4:
-4y / -4 = 8x / -4
y = -2x
The constant of variation is the coefficient of x, which is -2. Therefore, the correct answer is B) -2.
4. If y varies directly with x, it means that there is a constant ratio between y and x. In this case, we can express the relationship as y = kx, where k represents the constant of variation.
Given that y = 24 when x = 8, we can plug these values into the equation:
24 = k * 8
Solving for k:
k = 24 / 8
k = 3
Now that we have the value of k, we can use it to find y when x = 10:
y = k * x
y = 3 * 10
y = 30
Therefore, the correct answer is B) 30.
5. The equation of a line in slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept.
Given the slope 2/3 and the y-intercept 9, we can write the equation as:
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 passing through the points (1,-3) and (3,1), we need to find the slope (m) and the y-intercept (b).
Slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values, we get:
m = (1 - (-3)) / (3 - 1)
m = 4 / 2
m = 2
Now, we can use the slope-intercept form of a line and one of the given points (let's use (1,-3)):
y = mx + b
-3 = 2(1) + b
-3 = 2 + b
Solving for b:
b = -3 - 2
b = -5
Therefore, the equation of the line in slope-intercept form is:
y = 2x - 5.
Therefore, the correct answer is D) y = 2x - 5.