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1 year ago

Explain how the graph of y = 0.5x (the solid line on the graph) differs from the graph of y = x (the dashed line)

Mathematics

1 answer:

Fittoniya [83]1 year ago

8 0

Hello there. To solve this question, we'll have to see how to identify the difference between the two lines y = 0.5x (solid line) and y = x (the dashed line)

First, usually the solid line represents itself, all the values of y such that y = 0.5x.

In this case, for every value you take for x in the real line, you divide it by two and this will be its image, the line covers all the points satisfying this relation.

The dashed line usually represents inequalities, in this case, y is not equal to x.

When you have y > x, you have a dashed line and a shadowed region covering all the plane above the line.

When you have y < x, you have a dashed line and a shadowed region covering all the plane under the line.

When y is not equal to x, you only have a dashed line.

Therefore, the dashed line represents all the points in the plane such that y is equal to x, but excluding them in some sense.

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Can you explain how to do this

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Because I see a graph in the picture, I am assuming you need to graph the equations. The two equations are in slope-intercept form. They are in the form
y = mx + b

Where m is the slope and b is the y-intercept. That is why it is called the slope-intercept form.

If you want to graph a slope-intercept form equation, first plug in a value for x then compute it to get the y-coordinate.

First, let's get some points with the equation y = 4x + 3

We will plug in three values for x. 0, 1, and 2.

When x = 0

y = 4(0) + 3
y = 3

When x = 1

y = 4(1) + 3
y = 7

When x = 2

y = 4(2) + 3
y = 11

Now we have the points (0, 3), (1, 7), and (2, 11)

These points are called ordered pairs. Where the first number is the x-coordinate and the second number is the y-coordinate.

The ordered pairs tell you how many times you move your point away from the origin. The origin is (0, 0).

The first number of an ordered pair tells you how many times to move in the x direction and the second number how many times in the y direction.

Now graph the second equation. y = -x - 2

Just plug in some values for x.

I picked 0, 1, and 2.

When x = 0

y = 0 - 2
y = -2

When x = 1

y = -1 - 2
y = -3

When x = 2

y = -2 - 2
y = -4

Now we have the points (0, -2), (1, -3), and (2, -4)
Now plot those points and draw a line through them.

If you need to find the intersection of the equations y = 4x + 3 and y = -x - 2 you need to find where they intersect. Or in other words, share a common point.

After playing around with the numbers, I got the intersection point for the both of the equations.

It is the ordered pair (-1, -1). This the solution to both of the equations. If you plug in the ordered pairs into both of the equations, they will show it belongs to their graphs.

Plug in the values for y = 4x + 3

-1 = 4(-1) + 3
-1 = -4 + 3
-1 = -1

Plug in the values for y = -x - 2

-1 = -(-1) - 2
-1 = 1 - 2
-1 = -1

So, this ordered pair is on both equations!

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