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3 years ago

What are the slope and the y-intercept of the linear function that is represented by the table?

Mathematics

2 answers:

Lisa [10]3 years ago

7 0

Answer:

Step-by-step explanation:

The slope is -2/5, and the y-intercept is -1/3.

Hunter-Best [27]3 years ago

6 0

Answer:

Slope is -2/5 and y-intercept is -1/3

Step-by-step explanation:

To get the slope, we pick any two points and apply the slope formula

The slope formula is;

m = (y2-y1)/(x2-x1)

To get the slope, we select any two points

That will be;

(-3/4, -1/30) and (1/4,-13/30)

Substituting these in the slope formula, we have:

m = (-13/30 + 1/30)/(1/4 + 3/4)

m = 12/30 = -2/5

Generally, the equation of a straight line is;

y = mx + b

m is slope and b is the y-intercept

We already have the slope, to get the y-intercept, we select any of the points

-3/5 = -2/5(2/3) + b

= -3/5 + 4/15 = b

b = (-9 + 4)/15 = -5/15 = -1/3

Slope is -2/5 and y-intercept is -1/3

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3 years ago

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diamong [38]

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3 years ago

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2 years ago

3. Two cars are parked, 150m apart, and on opposite sides of a building. A camera on the top of the building rotates and can vie

allsm [11]

Answer:

The building is 61.5 m tall

Step-by-step explanation:

The image below is a diagram where all the given distances and angles are shown. We have additionally added some variables:

h = height of the building

a, b = internal angles of each triangle

x = base of each triangle

The angles a and b can be easily found by subtracting the given angles from 90° since they are complementary angles, thus:

a = 90° - 37° = 53°

b = 90° - 42° = 48°

Now we apply the tangent ratio on both triangles separately:

$\displaystyle \tan a=\frac{\text{opposite leg}}{\text{adjacent leg}}$

$\displaystyle \tan 53^\circ=\frac{150-x}{h}$

$\displaystyle \tan 48^\circ=\frac{x}{h}$

From the last equation:

$x=h.\tan 48^\circ$

Substituting into the first equation:

$\displaystyle \tan 53^\circ=\frac{150-h.\tan 48^\circ}{h}$

Operating on the right side:

$\displaystyle \tan 53^\circ=\frac{150}{h}-\tan 48^\circ$

Rearranging:

$\displaystyle \tan 53^\circ+\tan 48^\circ=\frac{150}{h}$

Solving for h:

$\displaystyle h=\frac{150}{\tan 53^\circ+\tan 48^\circ}$

Calculating:

h = 61.5 m

The building is 61.5 m tall

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