Determine if the equations below are proportional or not proportional.

y = 2/3x + 4

y = 1/2x

2x + 3y = 7

proportional because it crosses at the origin.

not proportional because it does not cross at the origin.

is not proportional.

is proportional

2x + 3y = 7 is not proportional.

Step-by-step explanation:

.  

This is an equation in the slope-intercept form and the y-intercept of the equation is (0,4).

Therefore, this equation does not pass through the origin.

So, the equation is not proportional.

This is also an equation in the slope-intercept form and the y-intercept of the equation is (0,0).

Therefore, this equation passes through the origin.

So, the equation is proportional.

2x + 3y = 7

⇒

This is also an equation in the slope-intercept form and the y-intercept of the equation is ().

Therefore, this equation does not pass through the origin.

So, the equation is not proportional.

(Answer)

1) y = 2/3x + 4,      y is NOT PROPORTIONAL to x.

2) y = 1/2x ,           y  is PROPORTIONAL to x.

3) 2x + 3y = 7 ,       y is NOT PROPORTIONAL to x.

Step-by-step explanation:

Two quantities P and Q  are said to be in proportion if one quantity is always a multiple of the other quantity.

or, P ∝ Q   ⇒   P  = k Q for some arbitrary constant k.

Here k = The Proportionality Constant.

Now, here

1) y = 2/3x + 4.

It is NOT of the form  y = kx

Hence, y is NOT PROPORTIONAL to x.

2) y = 1/2x

Here, It is  of the form  y = kx  where, k  = 1/2 ( Proportional Constant)

Hence, y is PROPORTIONAL to x.

3) 2x + 3y = 7

or, y = 1/3( 7-2x)

It is NOT of the form  y = kx

Hence, y is NOT PROPORTIONAL to x.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.