High School

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The relationship between a temperature in degrees Fahrenheit and its equivalent in degrees Celsius is given by the linear equation [tex]5F - 9C = 160[/tex], where [tex]F[/tex] is the temperature in degrees Fahrenheit and [tex]C[/tex] is the temperature in degrees Celsius.

A. Write the intercepts as points for this linear equation.

B. Create the graph of this equation using these intercepts.

Answer :

Sure! Let's solve this problem step-by-step.

We're given the linear equation that relates temperature in degrees Fahrenheit [tex]\( F \)[/tex] and degrees Celsius [tex]\( C \)[/tex]:

[tex]\[ 5F - 9C = 160 \][/tex]

### Part A: Write the intercepts as points

1. Find the [tex]\( F \)[/tex]-intercept:

To find the [tex]\( F \)[/tex]-intercept, set [tex]\( C = 0 \)[/tex] and solve for [tex]\( F \)[/tex].

[tex]\[ 5F - 9(0) = 160 \][/tex]

This simplifies to:

[tex]\[ 5F = 160 \][/tex]

Now, divide both sides by 5:

[tex]\[ F = \frac{160}{5} = 32 \][/tex]

So, the [tex]\( F \)[/tex]-intercept is the point [tex]\((32, 0)\)[/tex].

2. Find the [tex]\( C \)[/tex]-intercept:

To find the [tex]\( C \)[/tex]-intercept, set [tex]\( F = 0 \)[/tex] and solve for [tex]\( C \)[/tex].

[tex]\[ 5(0) - 9C = 160 \][/tex]

This simplifies to:

[tex]\[ -9C = 160 \][/tex]

Now, divide both sides by -9:

[tex]\[ C = \frac{160}{-9} \approx -17.78 \][/tex]

So, the [tex]\( C \)[/tex]-intercept is the point [tex]\((0, -17.78)\)[/tex].

### Part B: Create the graph using these intercepts

To graph the equation, you can plot the two intercept points on a coordinate plane:

- Plot the [tex]\( F \)[/tex]-intercept [tex]\((32, 0)\)[/tex] on the horizontal axis (Fahrenheit).
- Plot the [tex]\( C \)[/tex]-intercept [tex]\((0, -17.78)\)[/tex] on the vertical axis (Celsius).

Then, draw a straight line through these two points to represent the equation [tex]\( 5F - 9C = 160 \)[/tex].

These steps will help visualize the relationship between Fahrenheit and Celsius temperatures based on the given equation.

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Rewritten by : Barada

The F-intercept is at the point (32, 0) and the C-intercept is at the point (0, -17.78)

We are given the linear equation relating Fahrenheit (F) and Celsius (C):

5F - 9C = 160

To find the intercepts, we need to determine the points where the line crosses the F-axis (where C = 0) and the C-axis (where F = 0).

Set C = 0 and solve for F.

5F - 9(0) = 160

5F = 160

F = 160 / 5

F = 32

Set F = 0 and solve for C.

5(0) - 9C = 160

-9C = 160

C = -160/9

C ≈ -17.78