What is meant by the graph of a straight line?

Answer 1

A graph shows how two things are related to each other. A graph of "how fast someone runs" against " how old someone is" would go up for a while (as people become teenagers, they run more quickly), and then, after a maximum, start declining (60-year olds run less quickly than 50-year olds, 50-year olds rund less quickly than 30-year olds, and so forth.)

What a straight line graph shows is that the relationship between two things is both predictable and constant.

A good example would be a graph of "the amount of gasoline left in a car's gas tank" against "the number of miles you have driven."

You start out with a certain amount of gas in your tank, when zero miles are driven. That's the "b" in the "y = mx + b" equation. Then, as you drive a number of miles (that's the "x") you burn a certain amount of gas per mile (that's the "m," and since you're burning gas every mile, it subtracts from the amount of gas left, so it's negative), and "y" is the amount of gas left - less and less, as you drive more miles.

And the straight line shows that it doesn't matter how far you have driven, you will still burn the same amount of gas per mile, no matter how far you have driven.

It's actually a neat tool - when you draw the graph, the "b" (that is, the "y intercept") shows how much gas you had when you started. As you extend the line, you can see how much gas you have left after a certain number of miles. The "x intercept" shows how far you can go until you have run out of gas.

And the slope of the line - how slanted it is - shows how much gas you are burning per mile. If you wanted a very fuel-efficent car, you'd pick a car that had a very "gentle" slope - that is, it would not go down very quickly.

Not sure what else you need - but that's why we draw straight line graphs.

Answer 2

It means that growth of the y value for the function is proportionate to the growth of the x value.

The equation will look like y = mx + c,

where m is the slope value (slope is equal to height (y) divided by base width (x) of line)

and c is the value of y where the line intersects the y-axis.

The resultant graph will appear to be a straight line.

An example will be y = 2x + 3

For this graph, for each 2 points that y grows, x will grow 1 point. The +3 connotes that the resulting graph will intersect the y-axis at 3.

Answer 3

Well, the slope is constant, indicating a proportional relationship between X and Y

Answer 4

This means that it is a linear function, and thay y is proportional to x in some way.

Answer 5

Vertical, horizontal or diagonal, X is related proportionally to Y

Answer 6

That Y is proportional to X.