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2 years ago

The points (1, 5) and (0, –2) fall on a particular line. What is its equation in slope-intercept form?

Mathematics

1 answer:

Savatey [412]2 years ago

7 0

The equation of the line in slope intercept form is y = 7x - 2

<h3>How to find the equation of a line?</h3>

The equation of the line can be solved with the following equation.

y = mx + b

where

m = slope
b = y-intercept

Therefore,

m = -2 - 5 / 0 - 1 = -7 / -1

m = 7

Hence, using (1, 5)

y = 7x + b

5 = 7(1) + b

5 - 7 = b

b = -2

Therefore,

y = 7x - 2

Hence, the equation of the line in slope intercept form is y = 7x - 2

learn more on equation of a line here: brainly.com/question/14956513

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67. The line contains the point (4,0) and is parallel<br> to the line defined by 3x = 2y.

olganol [36]

Answer:

$y=\frac{3}{2} x-6$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form:

$y=mx+b$ where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)

Parallel lines will always have the same slope but different y-intercepts.

<u>1) Determine the slope of the parallel line</u>

Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.

$3x = 2y$

Switch the sides

$2y=3x$

Divide both sides by 2 to isolate y

$\frac{2y}{2} = \frac{3}{2} x\\y=\frac{3}{2} x$

Now that this equation is in slope-intercept form, we can easily identify that $\frac{3}{2}$ is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope $\frac{3}{2}$ . Plug this into $y=mx+b$ :

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

<u>2) Determine the y-intercept</u>

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

Plug in the given point, (4,0)

$0=\frac{3}{2} (4)+b\\0=6+b$

Subtract both sides by 6

$0-6=6+b-6\\-6=b$

Therefore, -6 is the y-intercept of the line. Plug this into $y=\frac{3}{2} x+b$ as b:

$y=\frac{3}{2} x-6$

I hope this helps!

7 0

3 years ago

A triangular field has sides 218.5 and 213.3 and the angle between them measures 58.96°. Find the area of the field.

Zolol [24]

Answer:

The area of the field = 19966.21 units²

Step-by-step explanation:

* Lets explain how to find area of a triangle by trigonometry rule

- In any triangle if you have the lengths of two sides and the measure

of the including angle between these two sides, then the area of the

triangle is A = $\frac{1}{2}s_{1}s_{2}sin\alpha$ , wher α is the

including angle between them

* Lets solve the problem

∵ The field is shaped triangle

∵ The lengths of two sides of the field are 218.5 and 213.3

∴ s1 = 218.5

∴ s2 = 213.3

∵ The measure of the angle between the two sides is 58.96°

∴ α = 58.96°

- Lets find the area using the rule of trigonometry

∴ $A=\frac{1}{2}(218.5)(213.3)sin(58.96)=19966.21$

∴ The area of the field = 19966.21 units²

4 0

3 years ago

What is the equivalent ratio of 26:7

anastassius [24]

Answer:

52 : 14

Step-by-step explanation:

multiply the numbers by 2

3 0

2 years ago

Find the mean of the data.<br><br> 9, 56, 24, 59, 2

timurjin [86]

Answer:

24 because it is the middle number

Step-by-step explanation:

5 0

2 years ago

Hamster heaven charges an annual fee of $20 plus $2.50 for each day of hamster activities you attend. Hamster fun world charges

GarryVolchara [31]

Answer: I wouldn’t be able to make a linear system right now, but it would be better to use Hamster Fun if it were long-term, and Hamster Heaven if it were short-term.

Step-by-step explanation:

HH (Hamster Heaven) charges 20$ plus one a day, and HF (the other) charges 35 plus one a day, so if you went for 80 days for either one:

HH: 20 + (2.50 x 80) =

20+200: 220

HF: 35 + (1 x 80)= 115

If it were for only a day or two, it would be more efficient to use Hamster Heaven.

7 0

3 years ago