Exercises: Linear functions and line equations

The line equation is: $y=\frac{5}{4}x-1$

You can read off the slope and the $y$-axis intercept of this graph from the equation.

$m=\frac{5}{4}\text{}$

$t=-1$

First check which functions have a $y$-intercept of $t=-1$ by reading off the $y-$value of each graph at the interaction with the $y$-axis.

Only graphs I and II have the $y-$intercept $-1$ so you can exclude any other graph.

Now check which of the two graphs has the slope $m=\frac{5}{4}$ by moving one to the right from the point $x=0$ and checking which of the two $y$-values increases by $\frac{5}{4}$.

Both graphs start at the point $P(0;-1)$. Since the straight line you are looking for has a slope of $\frac{5}{4}$, it also passes through the point $(0+4|-1+5)=(4|4)$.

But only line II is running through this point.

$\Rightarrow$   Graph II is the one belonging to the given equation.

Line to be checked: Graph III

First read off where the graph intersects the $y$-axis to find the $y$-axis intercept.

The $y$-value of the point where the $y$-axis is intersected amounts to $y=1.25$.

Now read off by how much the $y$-value changes when you go from $x=0$, one to the right. This will give you the slope.

The $y$-value increases from $y=1.25$ to $y=2.25$.

Thus the slope is $m=\frac{2.25-1.25}{1}=\frac{1}{1}=1$ .

Set up the line equation.

⇒ Graph III has the equation $y=x+1.25$