Exercises: Finding line equations

You are given the graph equation: $y=\frac{5}{4}x-1$

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

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

$\text{}t=-1$

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

Only graph 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 going one unit 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 $P(0;-1)$. As the straight line you are looking for has a gradient of $\frac{5}{4}$, 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 that belongs to the given equation.

We have to check graph III

First read where the graph intersects the y-axis to determine the y-intercept.

The y-value of the point where the y-axis is intersected is $y=1.25$. Therefore, $t=1.25$.

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

The y-value increases from $y=1.25$ to $y=2.25$. The gradient is therefore $m=\frac{\mathrm{2,25}-\mathrm{1,25}}{1}=\frac{1}{1}=1$ .

Set up the equation.

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