Q1. - Algebra 1

Question

The equation to convert Celsius temperature C to Kelvin K is shown. 

1. State the independent and dependent variables. Explain.
2. Determine the C- and K-intercepts mean in this situation.

Step-by-Step Solution

Answer

1. Independent variable in the given equation is C and the dependent variable is K.
2. The C-intercept is $\left(-273,0\right)$ and the K-intercept is $\left(0,273\right)$.

Part a. Step 1. State the concept of intercepts of a line.

The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis.

Then, algebraically,

 

• an x-intercept is a point on the graph where y is zero, and
• a y-intercept is a point on the graph where x is zero.

More specifically,

• an x-intercept is a point in the equation where the y-value is zero, and
• a y-intercept is a point in the equation where the x-value is zero.

Part a. Step 2. Use the given relation between K and C .

In the given relation $K=C+273$, it is clear that the value of Kelvin Temperature is depending on the value of the Celsius temperature.

So, Celsius temperature is the independent variable and the Kelvin temperature is the dependent variable.

Thus, C is the independent variable and K is the dependent variable.

Part b. Step 1. State the concept of intercepts of a line.

The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis.

Then, algebraically,

 

• an x-intercept is a point on the graph where y is zero, and
• a y-intercept is a point on the graph where x is zero.

 

More specifically,

 

• an x-intercept is a point in the equation where the y-value is zero, and
• a y-intercept is a point in the equation where the x-value is zero.

Part b. Step 2. Write the equation.

In the given relation $K=C+273$, it is clear that the value of Kelvin Temperature is depending on the value of the Celsius temperature.

So, Celsius temperature is the independent variable and the Kelvin temperature is the dependent variable.

Thus, C is the independent variable and K is the dependent variable.

Part b. Step 3. Calculation.

From the given graph is clear that the line intersects the horizontal line (C-axis) at the point $\left(-273,0\right)$, so the C-intercept is $\left(-273,0\right)$. It means when the Celsius temperature is $-273$, then the Kelvin temperature is 0.

 

Also, from the graph it is clear that the line intersects the vertical axis (K-axis) at the point $\left(0,273\right)$. So, it means when the Celsius temperature is 0, then the Kelvin temperature is 273.

 

Thus, C-intercept is $\left(-273,0\right)$ and the K-intercept is $\left(0,273\right)$.