Question

the temperature at sunrise is 42°F. each hour the temperature rises 6°F. write an equation that models the temperature y in degree farenheit after x hours . what is the graph of the equation

Answer 1

The Slope-Intercept form of an equation of a line is:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

According to the information given in the exercise, each hour the temperature rises 6 °F, then you can identify that the slope is:

`m=6`

Knowing that the temperature at sunrise is 42 °F, you can identify that the value of "b" is the following:

`b=42`

Then, the equation that models the temperature "y" (in degrees Farenheit) after "x" hours, is:

`y=6x+42`

In order to graph it, you can also find the x-intercept. By definition, when the line cuts the x-axis, the value of "y" is:

`y=0`

Substituting this value into the equation and solving for "x", you get:

`\begin{gathered} y=6x+42 \\ 0=6x+42 \\ -42=6x \\ \\ (-42)/(6)=x \\ \\ x=-7 \end{gathered}`

Knowing the y-intercept and the x-intecept, you can graph the equation.

The answers

- Equation:

`y=6x+42`

- Graph: