Question

At 2 hours before sunset, the temperature is 0°F. At 2 hours after sunset, the temperature is −4°F. Identify the slope, y-intercept, x-intercept, and equation that represents the temperature, y, as it changes over time, x.

Answer 1

The slope is 1, the y-intercept is 2, the x-intercept is -2, and the equation that represents the temperature change over time is y = x + 2.

Step-by-step explanation:

To find the equation that represents the temperature change over time, we need to first calculate the slope, y-intercept, x-intercept, and then form the equation.

Slope:

Subtract the temperature at 2 hours before sunset (-4°F) from the temperature at 2 hours after sunset (0°F): 0 - (-4) = 4.

Divide the temperature difference by the time difference (4 hours): 4 ÷ 4 = 1.

So, the slope (m) is 1.

Y-intercept:

Choose one of the temperature-time pairs. Let's use the temperature at 2 hours before sunset (0°F).

Substitute the temperature (0) as y and the corresponding time (-2) as x in the equation y = mx + b.

Solve for b: 0 = 1 * (-2) + b, which simplifies to b = 2.

Therefore, the y-intercept (b) is 2.

X-intercept:

Substitute 0 as y in the equation y = mx + b.

Solve for x: 0 = 1 * x + 2, which simplifies to x = -2.

The x-intercept is -2.

Equation:

Using the slope (m = 1) and y-intercept (b = 2), the equation that represents the temperature change over time is y = x + 2.

Answer 2

`Slope = -1`

`y = -2` --- y intercept

`x = -2` ---- x intercept

`y = -x - 2` --- equation

Step-by-step explanation:

Given

Represent temperature with y and time with x

When

`y = 0F; x = 2hrs\ before\ sunsets`

`y = -4F; x = 2hrs\ after\ sunset`

Solving Slope;

`Slope = (y_2 - y_1)/(x_2 - x_1)`

`Slope = (-4 - 0)/(2 - (-2))`

`Slope = (-4 - 0)/(2 +2)`

`Slope = (-4)/(4)`

`Slope = -1`

Using

`Slope = (y - y_1)/(x - x_1)`, we can get the equation

Where

`Slope = -1`

`x_1 = -2`

`y_1 = 0`

This gives:

`-1 = (y - 0)/(x -(-2))`

`-1 = (y)/(x +2)`

Cross multiply

`y = -x - 2`

Take x as 0; to solve the y intercept

`y = -0 - 2`

`y = -2`

Take y as 0; to solve the x intercept

`0 = -x -2`

`x = -2`