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Bond [772]
2 years ago
13

Can someone please tell me what the equation would be and how I would show it

Mathematics
1 answer:
slava [35]2 years ago
4 0

Answer:

Step-by-step explanation:

3x-4y-15=0

Geometric figure: Straight Line

Slope = 1.500/2.000 = 0.750

x-intercept = 15/3 = 5

y-intercept = 15/-4 = -3.75000

Step by step solution :

Step  1  :

Equation of a Straight Line

1.1     Solve   3x-4y-15  = 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 goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  3x-4y-15  = 0 and calculate its properties

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 15/-4 so this line "cuts" the y axis at y=-3.75000

y-intercept = 15/-4  = -3.75000

Calculate the X-Intercept :

When y = 0 the value of x is 5/1 Our line therefore "cuts" the x axis at x= 5.00000

x-intercept = 15/3  =  5

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -3.750 and for x=2.000, the value of y is -2.250. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.250 - (-3.750) = 1.500 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

  Slope     =  1.500/2.000 =  0.750

Geometric figure: Straight Line

Slope = 1.500/2.000 = 0.750

x-intercept = 15/3 = 5

y-intercept = 15/-4 = -3.75000

Hope This Helps!!!

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Answer:

\large\boxed{x=\dfrac{9}{8}-\dfrac{\sqrt{109}}{8},\ y=-\dfrac{1}{2}-\dfrac{\sqrt{109}}{18}}\\or\\\boxed{x=\dfrac{9}{8}+\dfrac{\sqrt{109}}{2},\ y=-\dfrac{1}{2}+\dfrac{\sqrt{109}}{18}}

Step-by-step explanation:

\left\{\begin{array}{ccc}4x\times9y=7&(1)\\4x-9y=9&(2)\end{array}\right\\\\(2)\\4x-9y=9\qquad\text{subtract}\ 4x\ \text{from both sides}\\-9y=-4x+9\qquad\text{change the signs}\\9y=4x-9\qquad\text{substitute it to (1)}\\\\4x(4x-9)=7\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\(4x)(4x)+(4x)(-9)=7\\(4x)^2-36x=7\\(4x)^2-2(4x)(4.5)=7\qquad\text{add}\ 4.5^2\ \text{to both sides}\\(4x)^2-2(4x)(4.5)+4.5^2=7+4.5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2

(4x-4.5)^2=7+20.25\\(4x-4.5)=27.25\to 4x-4.5=\pm\sqrt{27.25}\\\\4x-\dfrac{45}{10}=\pm\sqrt{\dfrac{2725}{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{2725}}{\sqrt{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25\cdot109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25}\cdot\sqrt{109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{5\sqrt{109}}{10}\qquad\text{add}\ \dfrac{45}{10}\ \text{to both sides}\\\\4x=\dfrac{45}{10}\pm\dfrac{5\sqrt{109}}{10}

4x=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 4}\\\\x=\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\\\\\text{Put the values of}\ x\ \text{to (2):}\\\\9y=4\left(\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\right)-9\\\\9y=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}-\dfrac{18}{2}\\\\9y=-\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 9}\\\\y=-\dfrac{1}{2}\pm\dfrac{\sqrt{109}}{18}

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