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3 years ago

1. Solve by graphing y = 3x – 5 y = -2x + 5

Mathematics

1 answer:

wariber [46]3 years ago

7 0

Answer:

Slope = 0.333/2.000 = 0.167

x-intercept = 5/-1 = -5.00000

y-intercept = 5/6 = 0.83333

Step-by-step explanation:

Step 1 :

Equation of a Straight Line

1.1 Solve 6y-x-5 = 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 6y-x-5 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 5/6 so this line "cuts" the y axis at y= 0.83333

y-intercept = 5/6 = 0.83333

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 = 5/-1 = -5.00000

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 0.833 and for x=2.000, the value of y is 1.167. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 1.167 - 0.833 = 0.333 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 0.333/2.000 = 0.167

Geometric figure: Straight Line

Slope = 0.333/2.000 = 0.167

x-intercept = 5/-1 = -5.00000

y-intercept = 5/6 = 0.83333

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Step-by-step explanation:

Here is the complete question

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.

y=35x; y=-0.05(x-400)²+9,492

what does the solution of the system represent in this context?

Solution

The solution of the system is obtained when both equations are equal. That is y=35x = y=-0.05(x-400)²+9,492 .

So, 35x = -0.05(x-400)² + 9,492.

Expanding the right side, we have

35x = -0.05(x² - 800x + 160000) + 9492

35x = -0.05x² -800x × -0.05 + (-0.05) × 160000 + 9492

35x = -0.05x² +40x - 8000 + 9492

35x = -0.05x² +40x + 1492

Collecting all the terms to the left side, we have

0.05x² - 40x - 1492 + 35x = 0

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The solution implies that the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

We confirm that by plugging in x = 229.83 in both equations.

y = 35x = 35(229.83) = 8044.05 ≅ 8044.1

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