Which of the following, Option 1 or Option 2, is a proportion?
Option 1: 5/6 = 15/18
Option 2: 5/6 =20/18
Option 1 is a proportion because both sides of the equation are equal to each other.
There are 48 inches in 4 feet, which is represented by the equation 4y=48x . Determine the number of inches per foot.
To determine the number of inches per foot, we need to find the value of y when x is equal to 1.
Given the equation 4y = 48x, we substitute x = 1:
4y = 48(1)
Simplifying, we have:
4y = 48
To isolate y, we divide both sides by 4:
y = 48/4 = 12
Therefore, there are 12 inches in 1 foot.
Write y−6x=5 in slope-intercept form
To write the equation y - 6x = 5 in slope-intercept form, which is y = mx + b, we need to isolate y on one side.
Let's begin by moving the -6x term to the right side of the equation:
y = 6x + 5
Now we have the equation in slope-intercept form, where the slope (m) is 6 and the y-intercept (b) is 5.
To determine whether Option 1 or Option 2 is a proportion, we need to check if the fractions on both sides of the equation are equal.
Let's start with Option 1: 5/6 = 15/18.
To compare these fractions, we can simplify them to their simplest form.
For 5/6, there are no common factors to simplify, so it remains as 5/6.
For 15/18, we can divide both the numerator (15) and denominator (18) by their greatest common divisor, which is 3.
Dividing 15 by 3 gives us 5, and dividing 18 by 3 gives us 6.
So, 15/18 simplifies to 5/6.
Since both sides of Option 1 are equal (5/6 = 5/6), it is a proportion.
Now let's move on to Option 2: 5/6 = 20/18.
Similarly, we can simplify both fractions.
For 5/6, it remains as 5/6 since there are no common factors to simplify.
For 20/18, we can simplify it by dividing both the numerator (20) and denominator (18) by their greatest common divisor, which is 2.
Dividing 20 by 2 gives us 10, and dividing 18 by 2 gives us 9.
So, 20/18 simplifies to 10/9.
Since 5/6 and 10/9 are not equal, Option 2 is not a proportion.
Therefore, Option 1 is a proportion, while Option 2 is not.