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My name is Ann [436]
3 years ago
9

Write an equation in slope-intercept form for the line with slope

Mathematics
1 answer:
mart [117]3 years ago
8 0
This would be easy for you if you know what the slope intercept form is.
y = mx + b this is the formula. M is where you put the slope and b is where the y-intercept goes. Now let's plug the numbers in. 
The slope you said is -23 so that goes into the place of m. X is the variable. I'll give you an example. Say Mary put $100 into her bank account and every week she took 23 dollars. x would the number of weeks because it can change. 
So back to plugging the numbers in. This is what it will look like when we put -23 in. 
y = -23x + b. As we said above, b is the y-intercept. This is the point where the line on the graph crosses the vertical line, which is y. x is the horizontal line.
You said the y-intercept is -4 so the line crosses the vertical line at the point -4. 
Plug this number into our formula, 
y = -23x + -4. 
There you go! We are finished making our slope intercept form equation.
I hope you understood, and good luck to you in the future. 
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Answer:

The matrix equation is \left[\begin{array}{ccc}1&1&1\\1&-1/2&0\\0&2&-1\end{array}\right]=\left[\begin{array}{c}120&35&20\end{array}\right]

Step-by-step explanation:

* Lets change the story problem to equations

- The distance between the starting point and checkpoint 1 is x

- The distance between checkpoint 1 to checkpoint 2 is y

- The distance between checkpoint and the finish line is z

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∴ x + y + z = 120 ⇒ (1)

-The distance from the starting point to checkpoint 1 is 35 miles

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∵ The distance from the starting point to checkpoint 1 is x

∵ The distance from checkpoint 1 to checkpoint 2 is y

- x is more than half y by 35

∴ x = 35 + (1/2) y ⇒ subtract (1/2) y from both sides

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- The distance from checkpoint 2 to the finish line is 20 miles less

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∵ The distance from checkpoint 2 to the finish line is z

∵ the distance from checkpoint 1 to checkpoint 2 is y

- z is less than twice y by 20

∴ z = 2y - 20 ⇒ add 20 to both sides

∴ z + 20 = 2y ⇒ subtract z from both sides

∴ 2y - z = 20 ⇒ (3)

* Now lets write the three equations

# x + y + z = 120 ⇒ (1)

# x - (1/2) y = 35 ⇒ (2)

# 2y - z = 20 ⇒ (3)

- Now lets write the matrix equation that models this situation

∴ \left[\begin{array}{ccc}1&1&1\\1&-1/2&0\\0&2&-1\end{array}\right]=\left[\begin{array}{c}120&35&20\end{array}\right]

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