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3 years ago

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

1 answer:

4 0

Answer:
$y = 2x - 5$

Explanation:

Slope-intercept form formula:
$y = mx + b$
For this formula we need the slope to find the slope use the slope formula:
$\frac{y_{2} - y}{x_{2} - x}$
Plug in the two points (1,-3) and (3,1)
$\frac{1 - - 3}{3 - 1}$
$\frac{4}{2}$
=2
the slope is 2

Now use the slope-interpect formula and plug in the slope (m)
$y = 2x + b$
plug in one point I'll use (3,1)
$1 = 2(3) + b$
1 = 6 +b
1-6=6-6+b
-5 = b

The equation would be:
$y = 2x - 5$

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Use an area model to solve. 1 3/4 X 2 1/2

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3 years ago

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vovikov84 [41]

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2 years ago

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The ideal width of a safety belt strap for a certain automobile is 7 cm. An actual width can vary by at most 0.3 cm. Write an ab

tester [92]

<span>
</span> $(7-.3) \leq w \leq (7+.3)
$

$6.7 \leq w \leq 7.3$

$w - 7 = -0.3$

$w = 6.7$

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<span>C. |w – 7| ≤ 0.3</span>

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3 years ago

−1/3−(−1/2)

Radda [10]

Hi ;-)

$-\frac{1}{3}-(-\frac{1}{2})=-\frac{1}{3}+\frac{1}{2}=-\frac{2}{6}+\frac{3}{6}=\frac{3}{6}-\frac{2}{6}=\frac{1}{6}\\\\3\frac{1}{3}-5=-(5-3\frac{1}{3})=-(4\frac{3}{3}-3\frac{1}{3})=-1\frac{2}{3}\\\\-1\frac{4}{5}-(-2\frac{7}{8})=-1\frac{4}{5}+2\frac{7}{8}=-1\frac{32}{40}+2\frac{35}{40}=2\frac{35}{40}-1\frac{32}{40}=1\frac{3}{40}\\\\-3\frac{3}{8}-\frac{7}{8}=-(3\frac{3}{8}+\frac{7}{8})=-3\frac{10}{8}=-3\frac{5}{4}=-4\frac{1}{4}\\\\4\frac{3}{4}-(-1\frac{1}{12})=4\frac{9}{12}+1\frac{1}{12}=5\frac{10}{12}$

6 0

2 years ago

can someone please help me figure this out? this is a summative and I'm failing for the year. it's algebra 1.

34kurt

Part (a)

x = number of bass caught
y = number of trout caught

x and y are nonnegative whole numbers.

3x represents the total weight of all the bass, since one bass weighs 3 pounds. Similarly, 2y is the total weight of the trout with each one being 2 pounds. Adding up all the weight of all the fish, we get 3x+2y. This is set equal to 34 pounds which is the total stated weight caught.

In short, we end up with the equation 3x+2y = 34

Now onto the second equation. The expression 5x represents how many points Pat gets from catching x bass, because he gets 5 points per bass. Then we subtract off 2y to represent Pat losing 2 points per trout he catches. Overall, his point total is 5x-2y. This is set equal to his point total of 14.

The second equation is 5x-2y = 14

------------

Answer:

3x+2y = 34

5x-2y = 14

Both equations are needed to form this particular system.

===================================================

Part (b)

We could use a number of methods to solve for (x,y). Possibly the most efficient is elimination. Why? Because note how we have 2y up top and -2y down below. They add to 0y which is just 0. The y terms go away, and are eliminated. Afterward, all we're left with is x in which we can solve for just like any other single variable equation. More info is in part (c).

===================================================

Part (c)

Refer to the answer in part (a). We'll add straight down. So that means we have these three sets of addition operations.

3x+5x becomes 8x
2y + (-2y), aka 2y-2y, becomes 0y and the y terms go away
34+14 simplifies to 48

After those three sets of addition operations, we're left with the much simpler equation 8x = 48. To solve this, we divide both sides by 8 and we get x = 6. This says Pat caught 6 bass.

Use this value of x to find y. So we'll plug x = 6 into either equation involving x,y and solve for y

3x+2y = 34

3(6)+2y = 34

18+2y = 34

2y = 34-18

2y = 16

y = 16/2

y = 8

So we can see that Pat caught 8 trout as well.

The check portion is shown in the attached image below. Effectively, all we're doing is replacing x and y with 6 and 8 respectively. Then we're simplifying both sides. Getting the same number on both sides results in a true equation, and therefore verifies we have the correct (x,y) solution.

Solution: (x,y) = (6,8)

Interpretation: Pat caught 6 bass and 8 trout

7 0

3 years ago