Understanding intercepts, like x-intercepts and y-intercepts, is really helpful when we use graphs to solve real-life problems.
So, what are intercepts?
An intercept is the spot where a graph touches an axis.
Let’s break it down into two types:
These are the points where the graph crosses the x-axis. This means that the output (y) equals zero.
Think of it like this: x-intercepts can show us when a business isn't making a profit or is just breaking even.
For example, if a company's money-making formula is shown as ( R(x) = 50x - 300 ), we can find the x-intercept by setting ( R(x) = 0 ).
Solving the equation ( 50x - 300 = 0 ) gives us ( x = 6 ).
This means that if the company sells 6 items, it will break even, meaning it doesn’t lose or gain money.
This point is where the graph crosses the y-axis. It shows us what the output is when the input (x) is zero.
For a formula like ( C(x) = 20x + 100 ), the y-intercept is found by looking at ( C(0) = 100 ).
This tells us that the starting cost, before selling anything, is £100.
Using these intercepts helps us picture things like costs and revenues.
This way, we can make smart choices based on where costs match revenues or when a project starts to make money.
Graphs are not just about numbers; they tell a story about how different things affect each other.
This helps guide our decisions using what we learn from math.
Understanding intercepts, like x-intercepts and y-intercepts, is really helpful when we use graphs to solve real-life problems.
So, what are intercepts?
An intercept is the spot where a graph touches an axis.
Let’s break it down into two types:
These are the points where the graph crosses the x-axis. This means that the output (y) equals zero.
Think of it like this: x-intercepts can show us when a business isn't making a profit or is just breaking even.
For example, if a company's money-making formula is shown as ( R(x) = 50x - 300 ), we can find the x-intercept by setting ( R(x) = 0 ).
Solving the equation ( 50x - 300 = 0 ) gives us ( x = 6 ).
This means that if the company sells 6 items, it will break even, meaning it doesn’t lose or gain money.
This point is where the graph crosses the y-axis. It shows us what the output is when the input (x) is zero.
For a formula like ( C(x) = 20x + 100 ), the y-intercept is found by looking at ( C(0) = 100 ).
This tells us that the starting cost, before selling anything, is £100.
Using these intercepts helps us picture things like costs and revenues.
This way, we can make smart choices based on where costs match revenues or when a project starts to make money.
Graphs are not just about numbers; they tell a story about how different things affect each other.
This helps guide our decisions using what we learn from math.