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artcher [175]
3 years ago
11

Write the equation of a line, in slope intercept form, that has a slope of 1 and passes through the point (2, 4).

Mathematics
2 answers:
rosijanka [135]3 years ago
7 0

The slope-intercept form:

y=mx+b

m - slope

b - y-intercept

We have the slope m=1\to y=1x+b=x+b

and point (2, 4). Substitute:

4=2+b      <em>subtract 2 from both sides</em>

2=b\to b=2

Answer: y=x+2

Fudgin [204]3 years ago
4 0

The answer is y=x+2 because you can put it into point slope form

y-4=1(x-2)simplify

y-4=x-2

y=x+2

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Answer:

(i) see first attached diagram

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<u />

<u>Part (i)</u>

see first attached diagram

<u>Part (ii)</u>

The angles marked in blue on the second attached diagram are Consecutive Interior Angles.  In this case they add to 180° as the North lines are parallel.

The sum of angles around a point is 360°

⇒ m∠QPR (shown in red on the second attached diagram) = 360 - 150 - (180 - 15) = 45°        

To calculate the distance between Q and R (marked in red on the attached diagram), use the cosine rule.

⇒ QR² = PR² + QP² - 2(PR)(QP)cos(QPR)

⇒ QR² = 32² + 24² - 2(32)(24)cos(45)

⇒ QR² = 513.8839841...

⇒ QR = √513.8839841...

⇒ QR = 22.67 km (2 dp)

<u>Part (iii)</u>

We need to find the angle marked in green on the third attached diagram.

To do this, we need to find the angle marked in pink and the angle marked in orange, then subtract them from 360°

Pink angle = 180 - 150 = 30° (using the same consecutive angle theorem as before)

Orange angle (o) using the sine rule:

⇒ sin(o)/32 = sin(45)/QR

⇒ sin(o) = 32sin(45)/22.67

⇒ sin(o) = 0.9981652337...

⇒ o = 86.52868176...°

Therefore, the green angle = 360 - 30 - 86.52868176... = 243° (nearest degree)

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