Exercises: Linear functions and line equations

Part 1:

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

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

First check for which functions the $y$-intercept is $t=-1$ by reading off the $y$-value of each graph at the intersection with the $y$-axis.

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

$t=-1$

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 $\frac{5}{4}$.

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

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

Only line II runs through this point.

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

Part 2:

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

The line to be checked is III

Now read off how much the $y$-value changes if you move one to the right starting from $x=0$ . This will give you the slope.

The $y$-value of the point the line intersects the $y$-axis is $y=1.25$.

Therefore, $t=1.25$.

Set up the line equation.

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

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

$\Rightarrow$ Graph III has the line equation $y=x+1.25$ .