Question

Does the point (5, 2) satisfy the equation y = 2x + –8?

Answer 1

The answer is:

y = 2x - 8

Work/explanation:

First, I simplify the right side of
`\sf{y=2x+(-8)}`.

I get :

`\sf{y=2x-8}`

Now, to determine if (5,2) satisfies y = 2x - 8, I plug in 5 for x and 2 for y:

`\sf{2=2(5)-8}`

Now simplify:

`\sf{2=10-8}`

`\sf{2\stackrel{\checkmark}{=}2}`

2 does equal 2, so the point (5,2) satisfies the equation y = 2x - 8.

Answer 2

Let us first understand what it means to satisfy the equation:

Satisfy: When we say that a point satisfies an equation, it means that when the x and y values of the point are substituted into the equation, both sides of the equation are equal.

To check if the point (5, 2) satisfies the equation y = 2x + -8, we substitute the x and y values of the point into the equation and see if both sides are equal.

Let's substitute x = 5 and y = 2 into the equation:

Left side: y = 2x + -8

y = 2(5) - 8

y = 10 - 8

y = 2

The left side of the equation evaluates to 2.

Now, let's compare this to the given y-value of the point:

Right side: y = 2

Since the y-value of the point (5, 2) is indeed 2, and both sides of the equation evaluate to 2, we can conclude that the point (5, 2) satisfies the equation y = 2x - 8.