Question

Find where the graphs intersect; f(x)=2x+3 and g(x)=-0.5x+7

Answer 1

Step 1

Given

`\begin{gathered} f(x)=\text{ 2x+3} \\ g(x)\text{ = -0.5x+7} \end{gathered}`

Required: To find where the graph of both functions intersect. In other words the find the value of x and hence f(x) and g(x).

Step 2

Solve both equations simultaneously.

`\begin{gathered} we\text{ will take f(x) and g(x) = y, so that} \\ y=2x+3\text{ -----(1)} \\ y=-0.5x+7----(2) \\ \end{gathered}`

Subtract equation 2 from 1

Hence,

`\begin{gathered} 4=\text{ 2.5x} \\ (4)/(2.5)=(2.5x)/(2.5) \\ x\text{ = 1.6} \end{gathered}`

Step 3

Check

`\begin{gathered} f(x)\text{ = 2x+3} \\ f(1.6)=\text{ 2(1.6) + 3 = 6.2} \\ g(x)=\text{ -0.5x+7} \\ g(1.6)=\text{ -0.5(1.6) +7 = 6.2} \\ \text{since the check gave us the same values, x = 1.6} \\ \text{And the coordinate point of the solution will be ( 1.6, 6.2)} \end{gathered}`

Hence the graph intersects at the point where x = 1.6 and y =6.2. Remember y = f(x) and g(x)