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vlabodo [156]
3 years ago
12

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

Mathematics
2 answers:
bekas [8.4K]3 years ago
8 0

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

GalinKa [24]3 years ago
7 0

Answer:

<h3>1. What is the slope of the line in the graph show below?</h3>

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.

<h3>2. Find the slope of a line that passes through (-2,-3), and (1,1). </h3>

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.

<h3>3. For the equation -4y = 8x, what is the constant of variation?</h3>

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.

<h3>4. Suppose y varies directly with x, and y = 24 when x = 8. What is the value of y when x = 10? </h3>

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.

<h3>5. What is an equation for the line with slope 2/3 and y-intercept 9?</h3>

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

<h3>6. What is an equation in slope-intercept form for the line that passes through the points (1,-3) and (3,1)?</h3>

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

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