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sattari [20]
3 years ago
13

A line passes through the point (2, 10) and has a y-intercept of 4. What is the equation of the line?

Mathematics
1 answer:
KatRina [158]3 years ago
3 0

Answer:

y=3x+4

Step-by-step explanation:

Hi there!

<u>What we need to know:</u>

  • Linear equations are typically organized in slope-intercept form: y=mx+b where m is the slope and b is the y-intercept (the value of y when x is equal to 0)

<u>1) Determine the slope (m)</u>

m=\frac{y_2-y_1}{x_2-x_1} where two points that the line passes through are (x_1,y_1) and (x_2,y_2)

We're given the point (2,10) and the y-intercept of 4. Recall that the y-intercept occurs when x is equal to 0. This means that the y-intercept occurs at (0,4), giving us our second point.

Plug these points into the equation

=\frac{10-4}{2-0}\\=\frac{6}{2}\\=3

Therefore, the slope of the line is 3. Plug this into y=mx+b

y=3x+b

<u>2) Determine the y-intercept (b)</u>

The y-intercept is given; it is 4. Plug this back into y=3x+b

y=3x+4

I hope this helps!

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Step-by-step explanation:

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4. The picture is fuzzy, but we think the lengths are 25 and 5. If they're something else, use the appropriate numbers. Using the same relations we used for problem 3,

y = √(5·25) = 5√5 . . . . . . . = √(short segment × hypotenuse)

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3 0
3 years ago
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Step-by-step explanation:

Hope this helps! :)

6 0
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5 0
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Please help me with 2 and 3 and use the elimination process!
grandymaker [24]

Answer:

2. Judy =$5

Ben= $4

Step-by-step explanation:

2. Let Judy =  x  and Ben =  y

8x + 10y = 80

9x + 5y = 65

Solve these simultaneous equations.

8 x  +  10 y  =  80

18 x  +  10 y  =  130

Take the second equation away from the first equation

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This means that Judy gets paid $5 an hour.

Therefore, Ben gets paid $4 an hour.

Answer:

3. 24 quarters and 16 dimes

Step-by-step explanation:

3. Let the number of dimes = x and the number of quarters = y

                                    Value      Value

Type        Number       of             of

of             of                EACH      ALL

coin         coins            coin        coins

-------------------------------------------

dimes         x              $0.10       $0.10x

quarters      y             $0.25      $0.25y

-------------------------------------------

TOTALS    40                            $7.60

x + y = 40

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Get rid of decimals by multiplying every term by 100:

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So we have the system of equations:

x + y = 40

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We solve by substitution.  Solve the first equation for y:

x + y = 40

y = 40 - x

Substitute (40 - x) for y in 10x + 25y = 760

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Substitute in y = 40 - x

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I hope that helped, sorry for taking so long :-)

8 0
3 years ago
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