What is a rational number?

1 answer:

8 0

Any number that can be rewritten as a simple fraction is a rational number. This means that natural numbers, whole numbers and integers, like 5, are all part of the set of rational numbers as well because they can be written as fractions, as are mixed numbers like 1 ½.

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Write the slope-intercept form of the equation of each line

Vera_Pavlovna [14]

First let's talk about the blue line.

You can see its rising so its slope is certainly positive. But by how much is it rising? You can observe that each unit it rises it goes 1 forward and 1 up so its slope is the ratio of 1 up and 1 forward which is just 1.

We have thusly,

$y=x+n$

Now look at where blue line intercepts y-axis, -1. That is our n.

So the blue line has the equation of,

$y=x-1$

Next the black lines. The black lines are axes so their equations are a bit different.

First let's deal with x-axis, does it have slope? Yes but it is 0. The x-axis is still, not rising nor falling. Where does x-axis intercept y-axis? At 0. So the equation would be,

$y=0x+0=0$

Now we have y-axis. Does y axis have a slope? Yes but it is $\infty$ . The y-axis rises infinitely in no run. Where does it intercept y-axis? Everywhere! So what should the equation be? What if we ask where does y-axis intercept x-axis and write its equation in terms of x. Y-axis intercepts x-axis at 0 which means its equation is,