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2 years ago

Write an equation in slope-intercept form for the graph shown. (1,0) (0,-2)

Mathematics

1 answer:

AlladinOne [14]2 years ago

4 0

Answer:

y= 2x -2

Step-by-step explanation:

Slope-intercept form

y= mx +c, where m is the slope and c is they y-intercept

$\textcolor{violet}{\text{\textcircled{1} Find the slope}}$

$\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }$

$slope = \frac{0 - ( - 2)}{1 - 0}$

$slope = \frac{0 + 2}{1}$

slope= 2

$\textcolor{violet}{\text{\textcircled{2} \text{Substitute value of slope into m}}}$

y= 2x +c

$\textcolor{violet}{\text{\textcircled{3} Find c}}$

Given that the y-intercept occurs at (0, -2), c= -2.

$\textcolor{violet}{\text{\textcircled{4} Substitute the value of c into the equation}}$

y= 2x -2

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3 years ago

xxMikexx [17]

Answer:

The similar triangles are Δ KMJ and Δ NML

The value of x is 3

KM = 6 and NM = 3

Step-by-step explanation:

* Lets revise the cases of similarity

1) AAA similarity : two triangles are similar if all three angles in the first

triangle equal the corresponding angle in the second triangle

- Example : In ΔABC and ΔDEF, m∠A = m∠D, m∠B = m∠E and

m∠C= m∠F then ΔABC ≈ ΔDEF by AAA

2) AA similarity : If two angles of one triangle are equal to the

corresponding angles of the other triangle, then the two triangles

are similar.

- Example : In ΔPQR and ΔDEF, m∠P = m∠D, m∠R = m∠F then

ΔPQR ≈ ΔDEF by AA

3) SSS similarity : If the corresponding sides of two triangles are

proportional, then the two triangles are similar.

- Example : In ΔXYZ and ΔLMN, if

then the two triangles are similar by SSS

4) SAS similarity : In two triangles, if two sets of corresponding sides

are proportional and the included angles are equal then the two

triangles are similar.

- Example : In triangle ABC and DEF, if m∠A = m∠D and

then the two triangles are similar by SAS

* Now lets solve the problem

- ∠KMJ is a aright angle and M is on JL

∴ m∠JML = 180° ⇒ straight angle

∵ m∠JMK + m∠LMN = m∠JML

∴ 90° + m∠NML = 180° ⇒ subtract 90° from both sides

∴ m∠NML = 90°

- In Δ KMJ and ΔNML

∵ m∠KMJ = m∠NML ⇒ proved

∵ m∠KJM = m∠NLM ⇒ given

- By using the second case above (AA similarity)

∴ Δ KMJ ≈ Δ NML

* The similar triangles are Δ KMJ and Δ NML

- From similarity

∴ Their sides are proportion

∴ $\frac{KM}{NM}=\frac{MJ}{ML}=\frac{KJ}{NL}$

∵ KJ = 10 and NL = 5

∵ KM = 3 + x and NM = x

- Substitute these values in the proportion relation

∵ $\frac{KM}{NM}=\frac{KJ}{NL}$

∴ $\frac{3+x}{x}=\frac{10}{5}$

- By using cross multiplication

∴ 5(3 + x) = 10(x) ⇒ simplify

∴ 5(3) + 5(x) = 10x

∴ 15 + 5x = 10x ⇒ subtract 5x from both sides

∴ 15 = 5x ⇒ divide both sides by 5

∴ 3 = x

* The value of x is 3

∵ KM = 3 + x

∵ x = 3

∴ KM = 3 + 3 = 6

∵ NM = x

∴ NM = 3

* KM = 6 and NM = 3

- Check the ratio

∵ KM/NM = 6/3 = 2

∵ KJ/NL = 10/5 = 2

∴ The sides are proportion

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4 years ago

Read 2 more answers

goverment winthrop called puritan massachusett"a______________" which meant it was a symbol to the rest of the world a city upon

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The answer is A.city upon hill

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4 years ago

P(Q) = 12/17 P(R) = 3/8 If Q and Rare independent events, find the PQ and R).

kodGreya [7K]

Answer:

9/34

Step-by-step explanation:

P(QnR) = P(Q) * P(R)

= 12/17 * 3/8

= 9/34

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2 years ago

A line has a slope of 1 and passes through the point (7,5). What is its equation in

GrogVix [38]

Answer:

$y=x-2$

Step-by-step explanation:

Slope-intercept form is $y=mx+b$ , so if $m=1$ , then we have $y=x+b$ and we'll need to plug in $(7,5)$ to get $b$ , the y-intercept:

$y=x+b$

$5=7+b$

$-2=b$

Therefore, the final equation in slope-intercept form is $y=x-2$

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2 years ago