In the standard (x,y) coordinate plane, if the x-coordinate of each point on a line is 4 less than twice its y-coordinate, what is the slope of the line?

you could just pick two points that satisfy your given condition,

pick any y,
e.g. y = 4, then x = 4 ---> (4,4)
y = 5, then 6 --> (6,5)

slope = (5-4)/(6-4) = 1/2

or

just translate "x-coordinate of each point on a line is 4 less than twice its y-coordinate"
---> x = 2y - 4
2y = x+4
y = (1/2)x + 2--- compare with y = mx + b
slope = 1/2

Q. A rectangular garden has a length of x and a width of y. The garden has its length reduced by 3 feet and its width extended by 2 feet. What is the area of the new garden?

Oh, the elusive slope! It's like trying to catch a slippery banana peel on a skateboard! Here we go:

If the x-coordinate of each point on a line is 4 less than twice its y-coordinate, we can express this mathematically as:

x = 2y - 4

Now, let's put this equation in slope-intercept form (y = mx + b), where m is the slope.

To do that, we'll rearrange the equation:

2y = x + 4

Divide both sides by 2 to solve for y:

y = (1/2)x + 2

And there we have it! The slope of the line is (1/2). Now, go forth and slay those math problems like the clown warrior you are! 🤡✨

To find the slope of a line, we need to have an equation representing the line. In this case, we know that the x-coordinate of each point on the line is 4 less than twice its y-coordinate.

Let's start by assigning variables to the coordinates. Let x represent the x-coordinate and y represent the y-coordinate. From the given information, we can write the following equation:

x = 2y - 4

Now we can rearrange the equation to solve for y in terms of x:

x + 4 = 2y
(1/2)(x + 4) = y

This equation represents the relationship between x and y on the line. The coefficient in front of x is the slope of the line. In this case, the slope is 1/2.

Therefore, the slope of the line is 1/2.