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WINSTONCH [101]
3 years ago
5

What is the equation for passing through (-2,2) and (5,3)

Mathematics
1 answer:
Reil [10]3 years ago
5 0
\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&&(~{{ -2}} &,&{{ 2}}~) 
%  (c,d)
&&(~{{ 5}} &,&{{ 3}}~)
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}\implies 
\cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{3-2}{5-(-2)}\implies \cfrac{3-2}{5+2}\implies \cfrac{1}{7}

\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=\cfrac{1}{7}[x-(-2)]
\implies 
y-2=\cfrac{1}{7}(x+2)
\\\\\\
y-2=\cfrac{1}{7}x+\cfrac{2}{7}\implies y=\cfrac{1}{7}x+\cfrac{2}{7}+2\implies y=\cfrac{1}{7}x+\cfrac{16}{7}
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2 years ago
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What is the rate of change for a linear function that passes through the points (8, -10) and (-6, 14)
Anna71 [15]

Answer: m=-1.714

Step-by-step explanation:

By definition, the slope of the line is described as "Rate of change".

You need to use the following formula to calcualte the slope of the line;

m=\frac{y_2-y_1}{x_2-x_1}

In this case you know that the line passes through these two points: (8, -10) and (-6, 14).

Then, you can say that:

y_2=-10\\y_1=14\\\\x_2=8\\x_1=-6

Knowing these values, you can substitute them into the formula for calculate the slope of a line:

 m=\frac{-10-14}{8-(-6)}

Finally, you must evaluate in order to find the slope of this line. You get that this is:

m=\frac{-24}{8+6}\\\\m=\frac{-24}{14}\\\\m=-\frac{12}{7}\\\\m=-1.714

8 0
3 years ago
Eva would like to buy a flute with an original price of $969.40. Which coupon should she use $75.00 off or 10% off
Dmitriy789 [7]

Answer:

10% off would be $96.94

So using the Coupon for 10% off would be the best deal.

8 0
3 years ago
What is the vertex form, f(x) = a(x - h)2-k, for a parabola that passes through the point (2,8) and has (1,0) as its
Novay_Z [31]

Answer:

Step-by-step explanation:

hello :

f(x) = a(x - h)²-k   ....vertex form  when the vertex is : (h,k)

h=1  and  k=0   so : f(x) = a(x-1)²

a parabola that passes through the point (2,8) : f(2)=8

a(2-1)² =8

a= 8

f(x) = 8(x-1)²=  8(x²-2x+1)

f(x) 8x²-16x+8   .....standard form

3 0
3 years ago
Eliza is two years younger than half her brother, Juan’s age. Write an equation to represent Eliza’s age. If Juan is 6 how old i
Natalka [10]
X = Juan's age
y = Eliza's age

Some key words/phrases we can use to help us make the equation are:

-is (whatever comes after this word usually equals the end result, or what it equals)
-two years younger
-than
-half her brother's age
.
just break it down :)

x/2 (half her brother's age) - 2 (two years younger) = y (Eliza is...)

| basically,
v

x/2 - 2 = y
So if Juan is 6, then we need to plug in 6 for x.

6/2 - 2 = y

3 - 2 = y

1 = y

ANSWER: Eliza is one year old.
6 0
3 years ago
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