All categories

3 years ago

Identify the equation of a line in slope-intercept form that is parallel to y = 2.5x + 5 and passes through (2, 3).

Mathematics

1 answer:

ser-zykov [4K]3 years ago

8 0

Answer:

The answer to your question is: y = 2.5x - 2

The first option is correct

Step-by-step explanation:

Data

Parallel to y = 2.5x + 5

Passes (2, 3)

Process

If the lines are parallel, they have the same slope.

slope = 2.5

(y - y1) = m (x - x1)

( y - 3) = 2.5 (x - 2)

y - 3 = 2.5x - 5

y = 2.5x - 5 + 3

y = 2.5x - 2

You might be interested in

let (-5,-7) be a point on the terminal side of theta. find the exact values of cos theta, sec theta, and cot theta

Svet_ta [14]

a. The exact value of cosθ = -5/√74

b. The exact value of secθ = -√74/5

c. The exact value of cotθ = 5/7

<h3>How to find the trigonometric ratios</h3>

Since the terminal side of the θ is the point, (-5, -7), we need to find the length of the terminal side.

So, r = √(x² + y²) where

x = -5 and
y = -7

So, r = √(x² + y²)

r = √((-5)² + (-7)²)

r = √(25 + 49)

r = √74

<h3>The value of the trigonometric ratio cosθ</h3>

Since the trigonometric ratio cosθ = x/r

Substituting the values of x and r into the equation, we have

cosθ = x/r

cosθ = -5/√74

So, the exact value of cosθ = -5/√74

<h3>The value of the trigonometric ratio secθ</h3>

Since the trigonometric ratio, secθ = r/x

Substituting the values of x and r into the equation, we have

secθ = r/x

secθ = √74/-5

secθ = -√74/5

So, the exact value of secθ = -√74/5

<h3>The value of the trigonometric ratio cotθ</h3>

Since the trigonometric ratio cotθ = x/y

Substituting the values of x and y into the equation, we have

cotθ = x/y

cotθ = -5/-7

cotθ = 5/7

So, the exact value of cotθ = 5/7

Learn more about trigonometric ratios here:

brainly.com/question/1518222

#SPJ1

3 0

2 years ago

If m∠a=47°, what is m∠b, m∠c, and m∠d? Explain how you know the measures are correct.

avanturin [10]

m ∠b = 133°, m ∠c = 47°, and m ∠d = 133°.

<h3>Further explanation</h3>

Follow the attached picture. I sincerely hope that's precisely a correct illustration.

We will use a graph of two intersecting straight lines.

Note that m ∠a and m ∠c are vertical angles. Since vertical angles share the same measures, in other words always congruent, we see $\boxed{ \ m \ \angle{c} = m \ \angle{a} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{c} = 47^0 \ }}$

We continue to determine m ∠b and m ∠d.

Note that m ∠b and m ∠d represent supplementary angles. Recall that supplementary angles add up to 180°.

Let us see the following steps.

$\boxed{ \ m \ \angle{a} + m \ \angle{b} = 180^0. \ }$

$\boxed{ \ m \ 47^0 + m \ \angle{b} = 180^0. \ }$

Both sides subtracted by 47°.

$\boxed{ \ m \ \angle{b} = 180^0 - 47^0. \ }$

Thus $\boxed{\boxed{ \ m \ \angle{b} = 133^0. \ }}$

Finally, note that m ∠b and m ∠d are vertical angles. Accordingly, $\boxed{ \ m \ \angle{d} = m \ \angle{b} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{d} = 133^0 \ }}$

<u>Conclusion:</u>

m ∠a = 47°
m ∠b = 133°
m ∠c = 47°
m ∠d = 133°

<u>Notes:</u>

Supplementary angles are two angles when they add up to 180°. $\boxed{ \ example: \angle{a} + \angle{b} = 180^0 \ }$
Vertical angles are the angles opposite each other when two lines cross. Note that vertical angles are always congruent, or of equal measure. $\boxed{ \ example: \angle{a} = \angle{c} \ }$

<h3>Learn more</h3>

About the measure of the central angle brainly.com/question/2115496
Undefined terms needed to define angles brainly.com/question/3717797
Find out the measures of the two angles in a right triangle brainly.com/question/4302397

Keywords: m∠a = 47°, m∠b, m∠c, and m∠d, 133°, vertical angles, supplementary, 180°, congruent

7 0

4 years ago

Read 2 more answers

(2,0) (4,5) write an equation that represents the line

Yuliya22 [10]

Answer:

the equation of the line in slope-intercept form would be y=5/2x-5

Step-by-step explanation:

hope this helped!! :D

4 0

3 years ago

Which graph is the solution of the following systems <br><br> HELP ON ON GRADPOINT

makkiz [27]

I think it is the second one but I’m not for sure I’m really just doing this for points

6 0

3 years ago

Which lines are perpendicular to the line y - 1 = 1/3 (x+2)? Check all that apply.

ioda

Answer: Options 1, 3, 5

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so since the slope of the given line is 1/3, we need to find lines with a slope of -3.

Option 1 has a slope of -3.
Option 2 has a slope of 3.
Option 3 has a slope of -3.
Option 4 has a slope of 1/3.
If we subtract 3x from both sides, we get y=-3x+7, so option 5 has a slope of -3.

7 0

2 years ago