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

Answer:

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

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{1-3}{1-0} =\frac{-2}{1}=-2$

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

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{1-(-3)}{1-(-2)} =\frac{1+3}{1+2}=\frac{4}{3}$

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 $y$

$-4y=8x\\y=\frac{8x}{-4}\\ y=-2x$

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 $m=\frac{2}{3}$ and $b=9$.

Replacing these values, we have

$y=mx+b\\\\\therefore y=\frac{2}{3}x+9$

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

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{1-(-3)}{3-1}=\frac{4}{2}=2$

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

$y=2x-5$