# How do I work out 5x+y=-10? I'm doing slope- intercept form at school and this is an example of one of them.

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Expert Answers

gsenviro | Certified Educator

The slope-intercept form of the equation of a line is typically written as,

y = mx + b

where, m is the slope of the line and b is the y-intercept (value of y when x=0).

You can rearrange your equation to this form.

For example, the given equation can be rewritten as:

5x + y = -10

or **y = -5x-10**

comparing this with the typical slope-intercept form of equation of line, we can see that

m = -5 and b = -10

So, by rearranging the given equation we can achieve the slope-intercept form and obtain the slope and intercept of the given line.

Student Comments

abusiveangel | Student

Hello dear, I will try to explain this to you in the most simplified way I could, so you understand it faster.
Lets's look at your example:
5x+y=-10
Looks vague right?
Now we should break it into pieces to understand what each part of the equation means. But first we have to re-write it in the correct formula (y=mx+b)
How do we do it?
Look at 5x+y=-10, it doesn't look like y=mx+b
We have to move 5x on the other side so we have only y on the left side
We subtract it from both sides
5x-5x+y=-10-5x
We have
y=-10-5x (remember we cannot add or subtract a number with a variable and its coefficient)
Still not perfectly polished... our last touch is to put the "mx" or the "-5x" before the y-intercept point or "-10"
Now it looks like this y=-5x-10, splendid!
Look at this:
y=-5x-10
y=mx+b
What do they mean?
mx is the slope, or rise/run (more details on the attached photo)
and b is the y-intercept or the point on the y axis (the vertical line on a plane graph)
I will teach you two ways to graph
First way (complicated and tiresome):
You can substitute for x and y with 2 pairs of points to draw the line with
First you pick a number for the input (x), it can be random
and you solve the the equation to find y
so in this example y=-5x-10, we can put 2 for the input
lets solve it, first substitute
y=-5(2)-10
Then solve
y=-10-10
y=-20
So now we know x=2 and y=-20 or points (2,-20)
And then you do it one more time
y=-5x-10
Let's put 3 for x
y=-5(3)-10
y=-15-10
y=-25
Points: (3,-25)
Then you simply graph (put the points and then connect them)
The simpler way:
y=-5x-10
First you find the y-intercept on the graph
10 points negative on the y-axis
You just put a point, then you go 5 points under the y-intercept or -15 on the y axis. Since we do not have a denominator or a "run", then we change it to 1. Remember all numbers divided by 1 are the same. The run is the point on the x-axis. We just go one point to the right if the denominator is not negative. Usually the negative sign is meant only for the numerator.
And then you have a new point (5 points under the y-intercept and one to the right) so we have (1,-15) and the first point (0,-10). That's it you just graph it. Check out the attachment, it shows exactly how you graph it.
Good Luck x :)