# How do you graph the line y=1/2x+5?

Jan 6, 2017

See explanation

#### Explanation:

As a minimum determine 2 points and draw a straight line through them. Extending the line to the borders of the graph paper. 3 points are better as it they should all line up. If not then something has been calculated incorrectly.

Set $x = 0$ giving:

$y = \frac{1}{2} \left(0\right) + 5$

So the first point is ${P}_{1} \to \left({x}_{1} , {y}_{1}\right) = \left(0 , 5\right)$

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Set $y = 0$ giving:

$0 = \frac{1}{2} x + 5$

Subtract 5 from both sides

$- 5 = \frac{1}{2} x$

Multiply both sides by $2$

$- 10 = x$

So the second point is ${P}_{2} \to \left({x}_{2} , {y}_{2}\right) = \left(- 10 , 0\right)$ Jan 6, 2017

I can't really write a short answer for graphs so....look down below :)

#### Explanation:

To graph this, you first have to graph the y intercept which is given.
Since the equation for slope intercept is y=mx+b
m is the slope which is $\frac{1}{2}$ and b is the y intercept which is $5$

Just remember "M" aka the number next to x is the slope and the number without any letter is the slope which is 5.

We can conclude 5 is "b" which is the y intercept.

So graph (0,5).

Next we use the "m" part which is the slope and in this case the slope is $\frac{1}{2}$

So we start from the y intercept (0,5) and do a format called "Rise over run" if you don't understand what this is you should go back to reviewing your notes! Because this is a very important part of math, which you should memorize.

If you still don't understand rise over run, maybe this will help

You rise up the elevator which is the top part of the slope (1) and then run to get to your meeting which is the bottom part of the slope (2).

Let me give you another example so you get the hang of it...So if the slope is $\frac{3}{4}$ You rise 3 (up the elevator) and run 4 (run to your meeting).

Now your probably confused! Which side am I supposed to go to the right?

or the left?

If the SLOPE is POSITIVE then the slope goes right.

If the SLOPE is NEGATIVE then the slope goes left.

So lets get back to the original question,

You graph the "b" part which is the y intercept, in this case 5. So graph (0,5).

Next you "Rise and Run" starting from the y intercept which is 0,5.

So you rise 1 because you are going up the elevator and run 2 (to the right) because you are running to your meeting.

Now if you want to go downwards instead of upwards you just do the opposite of rise and run DOWNWARDS.