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.