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KengaRu [80]
3 years ago
8

Find the equation, in slope-intercept form, of the line through the pair of points

Mathematics
1 answer:
ZanzabumX [31]3 years ago
5 0

Answer:

y=-\frac{3}{2}x+\frac{7}{2}

Step-by-step explanation:

We do not have enough information for slope intercept form. But we can use the point-slope formula to find the information. The formula is y -y_{1} =m(x -x_{1}) where we substitute a point (x,y) for (x_{1},y_{1}).  

We do not have m for the slope. But we do have (1,-2) and (-3, 4). We input the points for x_{1} =1\\y_{1}=-2 and x=-3\\y=4.  

(4-(-2))=m (-3-1)

We now simplify the parenthesis and solve for m.

(4+2)=m (-3+-1)\\6=m(-4)=

We divide by -4 on both sides and find m=-\frac{6}{4} =-\frac{3}{2}. We substitute m into the point slope form with one coordinate pair.

y-(-2)=-\frac{3}{2}(x-1)\\y+2=-\frac{3}{2}(x-1)\\y+2=-\frac{3}{2}x+\frac{3}{2}\\y+2-2=-\frac{3}{2}x+\frac{3}{2}-2\\y=-\frac{3}{2}x+\frac{3}{2}+\frac{4}{2} \\y=-\frac{3}{2}x+\frac{7}{2}

After simplifying the parenthesis, we subtracted 2 from both sides. We converted 2 into a fraction with 2 as the denominator.

This is slope intercept formy=-\frac{3}{2}x+\frac{7}{2}. The line has slope -3/2 and y-intercept (0,7/2) or b=7/2.

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Answer:

1,459,000

Step-by-step explanation:

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3 years ago
Ian tosses a bone up in the air for his dog, Spot. The height, h, in feet, that Spot is above the ground at the time t seconds a
kirill115 [55]

Answer:

12 feet per second.

Step-by-step explanation:

Please consider the complete question.

Ian tosses a bone up in the air for his dog, Spot. The height, h, in feet, that Spot is above the ground at the time t seconds after she jumps for the bone can be representedh(t)=-16t^2+20t.

What is Spot's average rate of ascent, in feet per second, from the time she jumps into the air to the time she catches the bone at t=1/2?  

We will use average rate of change formula to solve our given problem.

\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}

\text{Average rate of change}=\frac{h(\frac{1}{2})-h(0)}{\frac{1}{2}-0}

\text{Average rate of change}=\frac{-16\cdot(\frac{1}{2})^2+20\cdot \frac{1}{2}-(-16\cdot(0)^2+20\cdot (0))}{\frac{1}{2}-0}

\text{Average rate of change}=\frac{-16\cdot\frac{1}{4}+10-(0)}{\frac{1}{2}}

\text{Average rate of change}=\frac{-4+10}{\frac{1}{2}}

\text{Average rate of change}=\frac{6}{\frac{1}{2}}

\text{Average rate of change}=\frac{2\cdot 6}{1}

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Therefore, Spot's average rate of ascent is 12 feet per second.

3 0
3 years ago
Tell whether x and y show direct variation. Explain your reasoning. x=y+2
Mashutka [201]

Answer:

It does not show variation

Step-by-step explanation:

Given

x = y + 2

Required

Determine if there's direct variation between x and y

The general form of direct variation is:

y = kx

Make y the subject of formula in the given parameters;

x = y + 2

y = x - 2

Compare y = x - 2 to y = kx

<em>Since they are not of the same form, then the given equation do not show direct variation</em>

6 0
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A can of pineapple has a height of 13 cm and a diameter of 10 cm, What is the surface of the label that is on it in cm^2
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Answer:

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Step-by-step explanation:

Given data

Height= 13cm

Diameter= 10cm

Radius= D/2= 10/2= 5cm

The area of the curved surface will be = 2πr × h = 2πrh

substitute

Area of the curved surface = 2πrh= 2*3.142*5*13

Area of the curved surface = 2πrh= 408.46cm^2

Hence the area of the curve surface is 408.46cm^2

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Inside an auditorium, 1 out of 5 people wear hats, and 4 out of 5 people do not wear hats. Based on this information, predict ho
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Answer:

43

Step-by-step explanation:

4 0
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