## How can you determine if a graph is proportional?

**Plot**these points on the

**graph**. To

**determine whether**x and y have a

**proportional**relationship, see

**if**the line through these points passes through the origin (0, 0). The points are on a line that passes through the origin. So, x and y have a

**proportional**relationship.

## What does it mean for a graph to be proportional?

(Some textbooks describe a

**proportional**relationship by saying that ” y varies proportionally with x ” or that ” y**is**directly**proportional**to x .”) This**means**that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.## What does a proportional graph look like?

Key idea: the

**graph**of a**proportional**relationship is a straight line through the origin.## What does a non-proportional graph look like?

A

**non**–**proportional graph**is a straight line that**does**not go through the origin. How to tell the difference: A**proportional**table has a constant of proportionality in that y divided by x always equals the same value. A**non**–**proportional**table will have different values when y is divided by x.## What are 3 characteristics of a proportional relationship?

**proportional relationship**: Two quantities are said to have a

**proportional relationship**if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio.

**proportion**: An equation which states that two ratios are equal.

## What does a proportional relationship look like?

**Proportional relationships**are

**relationships**between two variables where their ratios are equivalent. Another way to think about them is that, in a

**proportional relationship**, one variable is always a constant value times the other. That constant is know

**as**the “constant of

**proportionality**“.

## Does a proportional relationship have to start at 0?

Directly

**proportional relationships**always pass through the origin (**0**,**0**). There are other linear**relationships**that**do**not pass through the origin.## How do you know if a relationship is non proportional?

**The graph of a linear equation is a line.**

- If b = 0 in a linear equation (so y = mx), then the equation is a
**proportional**linear**relationship**between y and x. - If b ≠ 0, then y = mx + b is a
**non**–**proportional**linear**relationship**between y and x.

## How do you know if a relationship is proportional?

How Do You

**Know If**Two Ratios are**Proportional**? Ratios are**proportional if**they represent the same**relationship**. One way to see**if**two ratios are**proportional**is to write them as fractions and then reduce them.**If**the reduced fractions are the same, your ratios are**proportional**.## How do you know if a relationship is proportional or Nonproportional?

Students should use their knowledge of

**proportional and non-proportional relationships**to**determine**when functions are**proportional**or**non-proportional**.**Proportional**functions will be in the form y = kx and**non-proportional**functions will be in the form y = mx + b.## How can you tell if a relationship is linear?

**How to Identify Linear Relationships**- The equation can have up to two variables, but it cannot have more than two variables.
- All the variables in the equation are to the first power. None are squared or cubed or taken to any power.
- The equation must graph as a straight line.

## What creates a linear relationship?

A

**linear relationship**is any**relationship**between two variables that**creates**a line when graphed in the x y xy xy -plane.**Linear relationships**are very common in everyday life.**Linear relationships**appear frequently on the SAT: about 25% of the SAT Math test involves**linear relationships**!## Does a linear relationship have to be proportional?

The

**relationship**between variables can be**linear**, non-**linear**,**proportional**or non-**proportional**. A**proportional relationship**is a special kind of**linear relationship**, but while all**proportional relationships are linear relationships**, not all**linear relationships are proportional**.## What is a negative linear relationship?

The slope of a line describes a lot about the

**linear relationship**between two variables. If the slope is**negative**, then there is a**negative linear relationship**, i.e., as one increases the other variable decreases. If the slope is 0, then as one increases, the other remains constant.## What does a negative linear relationship look like?

When one variable increases while the other variable decreases, a

**negative linear relationship**exists. The points in Plot 2 follow the line closely, suggesting that the**relationship**between the variables is strong.## Is a strong or weak correlation?

The

**Correlation**Coefficient When the r value is closer to +1 or -1, it indicates that there **is a stronger** linear relationship between the two variables. A **correlation** of -0.97 **is a strong** negative **correlation** while a **correlation** of 0.10 would be a **weak** positive **correlation**.

## How do you know if a relationship is non linear?

A

**nonlinear**curve may show a positive or a negative**relationship**. The slope of a curve showing a**nonlinear relationship**may be estimated by computing the slope between two points on the curve. The slope at any point on such a curve equals the slope of a line drawn tangent to the curve at that point.## How do you tell if an equation is linear or nonlinear?

Using an

**Equation** Simplify the **equation** as closely as possible to the form of y = mx + b. Check to see **if** your **equation** has exponents. **If** it has exponents, it is **nonlinear**. **If** your **equation** has no exponents, it is **linear**.

## How do you know if data is linear or nonlinear?

You can

**tell if**a table is**linear**by looking at how X and Y change.**If**, as X increases by 1, Y increases by a constant rate, then a table is**linear**. You can find the constant rate by finding the first difference. This table is**linear**.## What is the opposite of a linear relationship?

Any

**relationship**between two quantities that doesn’t fit the definition of a**linear relationship**is called a nonlinear**relationship**.David Nilsen is the former editor of Fourth & Sycamore. He is a member of the National Book Critics Circle. You can find more of his writing on his website at davidnilsenwriter.com and follow him on Twitter as @NilsenDavid.