Let's make the first equation the same as the second equation. Ok, so we know that the coefficients of x and y have to be the same. Because if a, b, and c were the same, you'd have the same line, which would give you infinitely many solutions. If you have two parallel lines (no solutions) than in the ax + by = c form, a and b are going to be the same, but c has to be different. So just to start, don't waste your time converting the equations to slope intercept form! That's a huge waste of time! Whew, I think that was the reciprocal you wanted to know about. That is 1/32 gallons used for every mile driven. If the car gets 32 miles of driving for every gallon, then one 32nd of every gallon is used every time the car drives a mile. Well, every mile driven will use a little bit of gas (hopefully a VERY little bit of gas). So, its meaning is 32 miles to the gallon, which is a different way of saying 32 miles per gallon. The only thing the question asks for is what the meaning of that 32 is in the denominator, and we just discovered that the units are miles per gallon. We discover that the units of the number in the denominator are miles per gallon (mpg) Isolate the units by dividing both sides by gallons Move the units out of the denominator by multiplying both sides by units We can use the rules of algebra to isolate for the units to figure out WHAT they are: That is where Sal has miles/units = gallons Gallons left = Starting gallons minus gallons usedĬool, so how do we figure out gallons used? All we know is that she drives m miles and we are told in the formula we are given that in the spot where we need gallons used we have miles divided by 32 somethings It says that the number of gallons left equals the total number held by the gas tank (15 gallons) minus a strange expression, m/32 The equation gives GALLONS left in her car. From the slope, we can see that every minute or change in x by 1, the car is traveling 2 miles or changing y by 2 miles. Slope is then calculated as 10miles / 5 minutes or 2 miles/minutes. On that interval, the change in y is (20 miles - 10 miles) and change in x is (15 min - 10 min). Slope is change in y divided by change in x. For example, if a car is at 10 miles from a house in 10 min and at 20 miles from a house at 15 min, then our interval of x values is 10 min - 15 min. We would divide that difference by the difference between the interval of x values we used. Assuming the graph is a straight line, if we want to find the slope we would find the difference between 2 y values on an interval of x values. We know that distance is dependent because time determines how much distance something will travel. Let's say that we have a graph of distance (y) and time (x). This simply means that if you have one variable that is dependent (y) on an independent variable (x), then the slope is given as change in y divided by change in x. Slope in math is defined as the rate of change of the y variable as x changes.
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