# Thread: linear lines and problems

1. ## linear lines and problems

hello i need help on a few quesitons.

the straight line with equation ax+by=c passes through the points (2,4) and (-3,1). find the values of a,b,c.

wheel rite, a small company that manufactures garden wheelbarrows, has overhead expenses of $30 000 per year. in addition, it cost$40 to manufacture each wheelbarrow
a- how many wheelbarrows must be made so that the overall cost is $46 per wheelbarrow? b- what is the minimum number of wheelbarrows that must be produced for wheel rite of make profit each year? thank you in advance 2. Originally Posted by white hello i need help on a few quesitons. the straight line with equation ax+by=c passes through the points (2,4) and (-3,1). find the values of a,b,c. The two co-ordinates are: $(2, 4)$ and $(3, -1)$. $m = \frac{y_1-y_2}{x_1 - x_2} = \frac{4-(-1)}{2-3} = \frac{5}{-1}= -5$ $y-y_1 = m (x - x_1) \implies y-4 = -5(x-2) \therefore y=-5x+14$. As $ax+by=c$ is $5x + y =14 \implies a=5, b=1, c=14$ 3. Originally Posted by white hello i need help on a few quesitons. the straight line with equation ax+by=c passes through the points (2,4) and (-3,1). find the values of a,b,c. Mr F says: There's not enough information to get unique numerical values of a, b and c. There's an infinite number of possible solutions. The best that can be done is to express two of a, b and c in terms of the third. Note: One of the infinite number of possible solutions is a = 5, b = 1, c = 14 (Given by Air). Another is a = 10, b = 2, c = 28 ....... wheel rite, a small company that manufactures garden wheelbarrows, has overhead expenses of$30 000 per year. in addition, it cost $40 to manufacture each wheelbarrow a- how many wheelbarrows must be made so that the overall cost is$46 per wheelbarrow?

Mr F says: Cost to make x wheel barrows is 30,000 + 40x. Therefore overall cost per barrow is (30,000 + 40x)/x. Solve (30,000 + 40x)/x = 46 ........

b- what is the minimum number of wheelbarrows that must be produced for wheel rite of make profit each year?

Mr F says: Are you selling at $46 per barrow? Then solve 46y > 30,000 + 40y for the smallest integer value of y. Note: You break even when y = x (the answer to a). thank you in advance .. 4. hey i found out y >5000 now what ? 5. Originally Posted by white hey i found out y >5000 now what ? If you sell at$46/barrow you make a profit when you sell more than 5000. So the minimum number you need to sell to make a profit is ....... ?