All courses › Mathematics 1P › Intersection

Intersection

Two linear offers cost the same where the graphs intersect. You set the expressions equal and solve for x. The steeper slope wins when x becomes large. To know which offer is cheaper on each side, you calculate the price at the intersection and compare one point to the left. x must make sense in the situation, for example a non-negative number.

a_1 x + b_1 = a_2 x + b_2

equal cost

x = \frac{b_1 - b_2}{a_2 - a_1}

intersection

Symbols

$a$	price per unit	NOK
$b$	fixed term	NOK

Example

Offer A is $100 + 5x$ and offer B is $40 + 8x$ .

$x = \dfrac{100 - 40}{8 - 5} = 20$ . The price there is $100 + 5 \cdot 20 = 200$ NOK.

Set the expressions equal. Check the answer in both offers.

Practise linear models and graphs for free →

← Inverse proportion · Probability and complement →

Part of Mathematics 1P: Linear models and graphs.