Question

1. find the following using the graph to the right

m = ______
the slope means

b = ______
the y-intercept means

equation:

what will be the tank temp after 8 hours?

tank temperature (graph: time (h) on x - axis, temperature (°f) on y - axis, starting at (0, 82) and decreasing)

1. find the follo

using the graph
right
m = ______
the slope mean
b = ______
the y - intercept
equation:
what will be le

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. From the graph, the y - intercept (when $x = 0$) is $y = 82$, so one point is $(0, 82)$. Let's take another point, say when $x = 1$, $y = 80$ (from the graph). Then $m=\frac{80 - 82}{1 - 0}=\frac{- 2}{1}=-2$. The slope means the temperature of the tank decreases by 2°F per hour.

Step2: Find the y - intercept (b)

The y - intercept is the value of $y$ when $x = 0$. From the graph, when $x = 0$, $y = 82$, so $b = 82$. The y - intercept means the initial temperature of the tank (at time $x = 0$ hours) is 82°F.

Step3: Write the equation

The equation of a line is $y=mx + b$. Substituting $m=-2$ and $b = 82$, we get $y=-2x + 82$.

Step4: Find the temperature after 8 hours

Substitute $x = 8$ into the equation $y=-2x + 82$. So $y=-2\times8+82=-16 + 82 = 66$.

Answer:

• $m=-2$ (The slope means the tank's temperature decreases by 2°F per hour)
• $b = 82$ (The y - intercept means the initial temperature of the tank is 82°F)
• Equation: $y=-2x + 82$
• Temperature after 8 hours: 66°F