The graph shows the number of gallons of water y in a...

The graph shows the number of gallons of water $y$ in a 100-gallon tank after $x$ minutes have elapsed. (Check your book to see graph) (a) Is water entering or leaving the tank? How much water is in the tank after 3 minutes? (b) Find the $x-$ and $y$ -intercepts. Interpret their meanings. (c) Find the slope-intercept form of the equation of the line. Interpret the slope. (d) Estimate the $x$ -coordinate of the point $(x, 50)$ that lies on the line.

The graph shows the number of gallons of water $y$ in a 100-gallon tank after $x$ minutes have elapsed.
(Check your book to see graph)

(a) Is water entering or leaving the tank? How much water is in the tank after 3 minutes?
(b) Find the $x-$ and $y$ -intercepts. Interpret their meanings.
(c) Find the slope-intercept form of the equation of the line. Interpret the slope.
(d) Estimate the $x$ -coordinate of the point $(x, 50)$ that lies on the line.

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Key Concepts

Linear Functions

Linear functions model relationships where the change between two variables is constant. They can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept, representing the starting value.

Slope

The slope of a line represents the rate of change between the independent and dependent variables. It quantifies how much the dependent variable increases or decreases for every one unit of change in the independent variable, with a positive slope indicating an increase and a negative slope indicating a decrease.

Intercepts

Intercepts are the points where a line crosses the axes. The y-intercept is the value of the dependent variable when the independent variable is zero, while the x-intercept is the value of the independent variable when the dependent variable is zero. These points help in understanding key values in the relationship modeled by the function.

Graph Interpretation

Graph interpretation involves extracting and understanding information such as the rate of change, initial conditions, and specific values represented by intercepts from a visual representation. It is a crucial skill for translating a graph into an equation and understanding the behavior of the underlying relationship.

Transcript

00:01 This we have a graph that's going to show the amount of water in a tank after x minutes have elapsed.

00:08 The first question says, is water entering or leaving the tank? we see as our time is increasing, our line is decreasing.

00:18 So water in gallons is going down, so we would say that water is leaving the tank.

00:25 Now, how much water is in the tank after 3 minutes? so time is on this bottom, so we're looking at 3 minutes.

00:32 When x is 3, we see our point right there.

00:35 It gives us that there is 70 gallons in the tank at 3 minutes.

00:41 Now we want to find our x and our y intercepts.

00:45 So our x intercept is going to be when the graph crosses the x axis, which looks like it's about 10.

00:53 And that's going to tell us that after 10 minutes, there is no water in the tank.

01:02 Now our y intercept is going to, i'm going to write this one up here, the y intercept is where the graph crosses the y axis, which is at 100.

01:18 And that's going to tell us that the gallon is going to start, so at 0 minutes, with 100 gallons of water.

01:33 Sorry, this should say the tank.

01:35 We're talking about a tank.

01:36 So the tank is going to start with 100 gallons of water.

01:41 Now we want to find the slope intercept form...

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