Suppose you take a road trip in an electric car. 143 miles into your trip, you see that the charge on the battery is at $69 \% .240 .1$ miles later, the charge reads $20 \%$.
(a) If $C$, the percent charge remaining on the battery, is linearly related to $d$, the distance driven (in miles), write a formula for the line $C=m d+b$.
\[
C=
\]
(b) How far can you travel (in total) until your battery runs out?

Step 1 ：We are given two points on the line: (143, 69) and (240.1, 20). We can use these points to find the slope of the line, which is given by the formula \(m = \frac{y2 - y1}{x2 - x1}\).

Step 2 ：Using the formula, we find that \(m = -0.5046343975283214\).

Step 3 ：Once we have the slope, we can use one of the points and the slope to find the y-intercept, \(b\), using the formula \(b = y - mx\).

Step 4 ：Using the formula, we find that \(b = 141.16271884654998\).

Step 5 ：Now that we have the slope and y-intercept, we can write the equation of the line as \(C = -0.5046343975283214d + 141.16271884654998\). This equation tells us the percent charge remaining on the battery after driving a certain distance.

Step 6 ：To find out how far we can travel until the battery runs out, we need to set \(C\) to 0 and solve for \(d\). This will give us the total distance we can travel on a full charge.

Step 7 ：Solving for \(d\), we find that \(d = 279.7326530612245\).

Step 8 ：Final Answer: The equation of the line is \(C = -0.5046343975283214d + 141.16271884654998\). You can travel approximately \(\boxed{279.73}\) miles in total until your battery runs out.