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den301095 [7]
2 years ago
5

Line passing through (0, 9) , (8, 7)

Mathematics
1 answer:
Aneli [31]2 years ago
5 0

<u>We are given:</u>

The 2 points through which the line passes through

(0,9) and (8,7)

__________________________________________________________

<u>Finding the equation of the line:</u>

To find the equation of the line, we will use the slope-intercept form:

y = mx + b           [where m is the slope and b is the y-intercept]

So, we need the slope and the y-intercept of the line in order to find the equation

<u>Finding the slope:</u>

We know that the slope of a line is:  change in y / change in x

So, Slope = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}

replacing the variables:

Slope = (7-9) / (8-0)

Slope =  -2 / 8

Slope = -1/4

<u>Finding the y-intercept:</u>

Since we know the slope, we know that the equation of the line will look like:

y=  (-1/4)x + b              [where b is the y-intercept]

we know that the ordered pair (0,9) will satisfy the equation since the line passes through that point

So, y = 9 and x = 0 will satisfy the equation:

9 = (-1/4)(0) + b

b = 9

Hence, the y-intercept is 9

<u>Equation of the line:</u>

We know that the general form of the slope-intercept form is:

y = mx + b                [where m is the slope and b is the y-intercept]

Since we know the values of the slope and the y-intercept:

y = (-1/4)x + 9

y = -x/4 + 9 is the equation of the line that passes through the given points

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Brrunno [24]

Answer:

x=4

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Step-by-step explanation:

we have the following equations

3x+y=15  equation 1

5x-4y=8  equation 2

using equation 1 we have:

y=15-3x equation 3

using equation 3 in equation 2 we have:

5x-4(15-3x)=8

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5x-60+12x = 8

17x=68

x=68/17

so we have x=4

finally in equation 3:

y = 15-3(4)

y = 15-12

y = 3

8 0
3 years ago
Carrie did sit-ups every for 5 days. The number of sit-ups she did on each day is shown on the table.
Nataly [62]

Answer:

32

Step-by-step explanation:

I mutiplied 2 to the 5th power and it equals 32

7 0
2 years ago
3/a times x-4=20<br> What is x?
spin [16.1K]

Answer:

Step  1  :

           3

Simplify   —

           a

Equation at the end of step  1  :

   3                

 ((— • x) -  4) -  20  = 0  

   a                

Step  2  :

Rewriting the whole as an Equivalent Fraction :

2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  a  as the denominator :

        4     4 • a

   4 =  —  =  —————

        1       a  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3x - (4 • a)     3x - 4a

————————————  =  ———————

     a              a    

Equation at the end of step  2  :

 (3x - 4a)    

 ————————— -  20  = 0  

     a        

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  a  as the denominator :

         20     20 • a

   20 =  ——  =  ——————

         1        a    

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

(3x-4a) - (20 • a)     3x - 24a

——————————————————  =  ————————

        a                 a    

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  3x - 24a  =   -3 • (8a - x)  

Equation at the end of step  4  :

 -3 • (8a - x)

 —————————————  = 0  

       a      

Step  5  :

When a fraction equals zero :

5.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 -3•(8a-x)

 ————————— • a = 0 • a

     a    

Now, on the left hand side, the  a  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  -3  •  (8a-x)  = 0

Equations which are never true :

5.2      Solve :    -3   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Equation of a Straight Line

5.3     Solve   8a-x  = 0 Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK). "y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.In this formula :y tells us how far up the line goesx tells us how far alongm is the Slope or Gradient i.e. how steep the line isb is the Y-intercept i.e. where the line crosses the Y axisThe X and Y intercepts and the Slope are called the line properties. We shall now graph the line  8a-x  = 0 and calculate its properties

Graph of a Straight Line :

 

 

Calculate the Y-Intercept :

Notice that when x = 0 the value of a is 0/8 so this line "cuts" the a axis at a= 0.00000

 a-intercept = 0/8  =  0.00000  

Calculate the X-Intercept :

When a = 0 the value of x is 0/-1 Our line therefore "cuts" the x axis at x=-0.00000

 x-intercept = 0/-1  = -0.00000  

Calculate the Slope :

Slope is defined as the change in a divided by the change in x. We note that for x=0, the value of a is -0.000 and for x=2.000, the value of a is 0.250. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 0.250 - -0.000 = 0.250 in a. (The change in a is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  0.250/2.000 =  0.125  

Geometric figure: Straight Line

 Slope = 0.250/2.000 = 0.125

 x-intercept = 0/-1 = -0.00000

 a-intercept = 0/8 = 0.00000

Step-by-step explanation:

8 0
3 years ago
Correct answer gets Brainliest! Solve for x.
Simora [160]

Subtract 13 from both sides:

-7-13 \geq -5x

-20 \geq -5x

Divide both sides by -5. Since this is a negative number, you have to invert the inequality sign:

4 \leq x

Which means

x \geq 4

4 0
3 years ago
Read 2 more answers
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lianna [129]

Answer:

444,444

Step-by-step explanation:

total amount=737373

jerry=292929

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To figure the amount of video games Brandon has, we have to subtract the amount of both he and his friend altogether amount with Jerry's current amount of video games.

737,373-292,929=444,444

So, by subtracting the two, the answer would be 444,444.

Brandons total amount of video games:444,444

5 0
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