Question

1. What is the slope of the line in the graph show below?

(Image)
A. -2
B. -1
C. 1
D. 2

2. Find the slope of a line that passes through (-2,-3), and (1,1).

3. For the equation -4y = 8x, what is the constant of variation?

4. Suppose y varies directly with x, and y = 24 when x = 8. What is the value of y when x = 10?

5. What is an equation for the line with slope 2/3 and y-intercept 9?

6. What is an equation in slope-intercept form for the line that passes through the points (1,-3) and (3,1)?

Answer 1

What is the slope of the line in the graph show below? c1

Answer 2

1. What is the slope of the line in the graph show below?

The line intercepts points (0,3) and (1,1).

We can find the slope using its formula

`m=(y_(2)-y_(1) )/(x_(2)-x_(1) )=(1-3)/(1-0) =(-2)/(1)=-2`

Therefore, the slope is -2. The right answer is A.

2. Find the slope of a line that passes through (-2,-3), and (1,1).

To find the slope, we apply the same formula as we did in the first question

`m=(y_(2)-y_(1) )/(x_(2)-x_(1) )=(1-(-3))/(1-(-2)) =(1+3)/(1+2)=(4)/(3)`

Therefore, the slope is 4/3.

3. For the equation -4y = 8x, what is the constant of variation?

To find the constant of variation, we need to express the given linear equation in the form
`y=mx+b`. That is, we need to isolate
`y`

`-4y=8x\\y=(8x)/(-4)\\ y=-2x`

Where
`m=-2` and
`b=0`.

Therefore, the constant of variation is -2.

4. Suppose y varies directly with x, and y = 24 when x = 8. What is the value of y when x = 10?

This problem is setting a proportionality, that is, the raltion between the first pair of coordinates is the same for the second pair.

So, if y = 24 when x = 8, that means y-values are triple than x-values, because 8x3 = 24.

Now, if x = 10, then y = 3x10 = 30.

Therefore, the missing value is y = 30.

5. What is an equation for the line with slope 2/3 and y-intercept 9?

To find the equation, we use the slope-intercept formula

`y=mx+b`

Where
`m` is the slope and
`b` is the y-intercept.

In this case, we have
`m=(2)/(3)` and
`b=9`.

Replacing these values, we have

`y=mx+b\\\\\therefore y=(2)/(3)x+9`

6. What is an equation in slope-intercept form for the line that passes through the points (1,-3) and (3,1)?

First, we need to find the slope

`m=(y_(2)-y_(1) )/(x_(2)-x_(1) )=(1-(-3))/(3-1)=(4)/(2)=2`

Then, we use the point-slope formula

`y-y_(1) =m(x-x_(1) )\\y-1=2(x-3)\\y=2x-6+1\\y=2x-5`

Therefore, the slope-intercept form is

`y=2x-5`