Linear equations  (Page 4/6)

Substituting the point (2, 3) and $m=-3/5$ in the point-slope formula, we get

Multiplying both sides by 5 gives us

The point-slope form is

Multiplying both sides by 3 gives us

We should always be able to convert from one form of an equation to another. That is, if we are given a line in the slope-intercept form, we should be able to express it in the standard form, and vice versa.

Multiplying both sides of the equation by 3, we get

Solving for $y$ , we get

1. $A=3$ , $B=-5$ , therefore, $m=-\frac{3}{-5}=\frac{3}{5}$
2. $A=2$ , $B=7$ , therefore, $m=-\frac{2}{7}$
3. $m=-\frac{4}{-3}=\frac{4}{3}$

Since the slope of the line is $-4/5$ , we know that the left side of the equation is $\mathrm{4x}+\mathrm{5y}$ , and the partial equation is going to be

Of course, $c$ can easily be found by substituting for $x$ and $y$ .

The desired equation is

In this problem, $0.50 per mile is referred to as the variable cost , and the flat charge $5 as the fixed cost . Now if we look at our cost equation $y=\text{.}\text{50}x+5$ , we can see that the variable cost corresponds to the slope and the fixed cost to the y-intercept.

The fact that the variable cost represents the slope and the fixed cost represents the y-intercept, makes $m=\text{10}$ and $y=\text{2500}$ .

Therefore, the cost equation is $y=\text{10}x+\text{2500}$ .