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3 years ago

How to find the slope of a line on a coordinate plane?

1 answer:

5 0

The slope of a line is the ratio of vertical travel to horizontal travel, whether on a coordinate plane or in the real world. It can be positive or negative.

On an x-y plane, to find the slope of a line you would identify the coordiates of two points on the line, then form the ratio
slope = (difference of y-coordinates)/(difference of corresponding x-coordinates)

Given two points (x1, y1) and (x2, y2), the slope is computed as
slope = (y2 - y1)/(x2 - x1)

The points can be used in the computation in either order and the result will be the same. It is often convenient to have x2 > x1, so the denominator is positive. This can reduce errors in the arithmetic, but it is not required.

If the line is a vertical line, so that all x-values are the same, the slope is said to be "undefined."

On a conventionally drawn coordinate plane, a line with positive slope will go up to the right (/); a line with negative slope will go down to the right (\).

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Subtract (x^2-5x+4)-(8x-9)

cluponka [151]

Answer: x^2 - 13x + 13

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A taxi company charges a $2.00 base fare plus an additional fare based on a per-mile rate and a per-minute rate. Ryan's first ta

Fed [463]

A $2.00 base fare charge, and per-mile, and per-minute rates related as follows; 3•x + 7•y = 6.5 and 7•x + 14•y = 14, give the distance traveled in the third ride as 4.5 miles

<h3>How can the length of the third ride be calculated?</h3>

The base fare = $2.00

Let x represent the per-mile rate, and let y represent the per-minute rate, we have;

The cost of Ryan's first taxi ride = $8.50

Distance traveled in the first ride = 3.0 miles

Time taken during the first ride = 7 minutes

Therefore;

2 + 3•x + 7•y = 8.5

Which gives;

3•x + 7•y = 8.5 - 2 = 6.5

3•x + 7•y = 6.5...(1)

Distance traveled in the second ride = 7.0 miles

Duration of the second ride = 14 minutes

The second ride cost = $16.00

Therefore;

2 + 7•x + 14•y = 16

Which gives;

7•x + 14•y = 16 - 2 = 14

7•x + 14•y = 14...(2)

Solving the above simultaneous equations by multiplying equation (1) by 2 then subtracting the result from equation (2) gives;

(7•x + 14•y) - 2 × (3•x + 7•y) = 14 - 2×6.5 = 1

x = 1

The per-mile rate, x = $1

3•x + 7•y = 6.5

7•y = 6.5 - 3•x

7•y = 6.5 - 3×1 = 3.5

y = 3.5/7 = 1/2 = 0.5

The per-minute rate, y = $0.5

Duration of the third taxi ride = 10 minutes

Cost of the third ride = $13.50

Therefore;

2 + 1×a + 10×y = $13.50

Where a is the distance traveled during the third ride, we have;

2 + 1×a + 10×0.5 = $13.50

2 + a + 5 = 13.5

a = 13.5 - 2 - 7 = 4.5

The third ride was, a = 4.5 miles

Learn more about simultaneous linear equations here:

brainly.com/question/24085666

#SPJ1

3 0

2 years ago

Solve the following system of equations. 2x+y=3 I= 2y - 1 x= y=

marin [14]

Note: I am assuming your second equation is:

x = 2y - 1

Answer:

The solution to the system of equations is:

x = 1

y = 1

Step-by-step explanation:

Given the system of equations

2x+y=3

x = 2y - 1

solving the system of equations using the elimination method

$\begin{bmatrix}2x+y=3\\ x=2y-1\end{bmatrix}$

Arrange equation variables for elimination

$\begin{bmatrix}2x+y=3\\ x-2y=-1\end{bmatrix}$

Multiply x-2y=-1 by2: 2x-4y=-2

$\begin{bmatrix}2x+y=3\\ 2x-4y=-2\end{bmatrix}$

subtracting the equations

$2x-4y=-2$

$-$

$\underline{2x+y=3}$

$-5y=-5$

now solve -5y = -5 for y

$-5y=-5$

Divide both sides by -5

$\frac{-5y}{-5}=\frac{-5}{-5}$

Simplify

$y=1$

For 2x+y=3 plug in y=1

$2x+1=3$

subtract 1 from both sides

$2x+1-1=3-1$

Simplify

$2x=2$

Divide both sides by 2

$\frac{2x}{2}=\frac{2}{2}$

Simplify

$x=1$

Therefore, the solution to the system of equations is:

x = 1

y = 1

8 0

3 years ago

A computer repairman charged $720 to come visit a business, plus $45 per hour of work. During one week he earned $1,800. How man

Anvisha [2.4K]

Answer:

24 hours

Step-by-step explanation:

Hi,

The equation to represent this situation would be 45x + 720 = 1800

(45 is the cost per hour, x is the number of hours since you don't know how many hours that person was there for. 720 is there because no matter what, you have to pay 720 to visit and = 1800 is the total cost)

Now, solve for x.

45x + 720 = 1800

Subtract 720 on both sides...

45x = 1080

Divide by 45 on both sides...

x = 24

He worked 24 hours that week.

Hope this helps :)

6 0

3 years ago

Read 2 more answers

Rewrite with only sinx and cosx. Cos2x - sinx

Margarita [4]

Cos2x= 1 - 2sin $x^{2}$ x
subtract sinx to finsih

3 0

3 years ago