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Exercises: Linear functions and line equations

Determine the function equation.

A straight line has the $y$ -axis intercept $t$ and passes through the point $P$ . Determine the function equation $f (x)$ and draw the graph.

$t = - 1$ $P = (2 | 3)$

For this task you need the following basic knowledge: Linear function
Determining the function equation
General line equation:
$y = m \cdot x + t$
Substitute $t$ into the line equation.
$f (x) = m \cdot x - 1$
Now plug the point $P$ into $f (x)$ .
$3 = m \cdot 2 - 1$
Solve for $m$ .
$m = (3 + 1) : 2 = 2$
$f (x) = 2 x - 1$
Plot:
$t = 3$ $P (- 4 | - 3)$

For this task you need the following basic knowledge: Linear function
Determining the function equation
General line equation:
$y = m \cdot x + t$
Substitute $t$ into the line equation.
$f (x) = m \cdot x + 3$
Now plug the point $P$ into $f (x)$ .
$- 3 = m \cdot (- 4) + 3$
Solve for $m$ .
$m = \frac{- 6}{- 4} = \frac{3}{2}$
$f (x) = \frac{3}{2} x + 3$
Plot:

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