Question

Graph each equation. Decide whether each graph represents a linear or nonlinear function

$$\begin{gathered} \mathrm{h}=5+6\mathrm{t} \\ \mathrm{h}=5+6{\mathrm{t}}^2 \end{gathered}$$

Answer 1

Step 1: Graph the equation: $\mathrm{h}=5+6\mathrm{t}$.

Lets, $\mathrm{h}=0$

$$\begin{gathered} \Rightarrow 0=5+6\mathrm{t} \\ \Rightarrow 6\mathrm{t}=-5 \\ \Rightarrow \mathrm{t}=-\frac{5}{6}=-0.833 \end{gathered}$$

we get, $\mathrm{t}=-\frac{5}{6}$ so, coordinate is $\left(0,-\frac{5}{6}\right)$.

Now let, $\mathrm{t}=0$

$$\begin{gathered} \mathrm{h}=5+6\mathrm{t} \\ =5+6\times 0 \\ =5 \end{gathered}$$

we get, $\mathrm{h}=5$ so, coordinate is $\left(5,0\right)$.

Graph will be,

We know, a linear function is a function whose graph is a straight line.

Hence, Yes, it’s a linear function.

Step 2: Graph the equation: $\mathrm{h}=5+6{\mathrm{t}}^2$.

A linear function can be described by a linear equation and a linear equation is a degree-$1$ polynomial.

Also, a linear equation has the form:$\mathrm{y}=\mathrm{mx}+\mathrm{c}$ where $\mathrm{m}$ is the slope, $c$ is the constant.

The following is not a linear equation: $\mathrm{h}=5+6{\mathrm{t}}^2$ because the term $6{\mathrm{t}}^2$ has degree $2$.

Hence, this is represents a nonlinear function.