How do I graph -3x + 5y = -10

Question

Each axis is one unit

Answer 1

Almost all lines can be graphed by finding two points, called the intercepts. 

(This applies to linear equations in which there are both x and y terms.)

 

Choose x = 0, substitute, and solve for y; that will be the "y intercept."

 

Choose y = 0, substitute, and solve for x; that will be the "x intercept."

 

Mark those two points on the axes and draw (accurately) a st. line passing through these points.

 

P.S.: your statement "each axis is one unit" is not clear and is not necessary.  Did you mean that the graph should have identical scales on each axis?

Answer 2

So, in order to graph this function with the greatest ease, one should put the equation in another form (y=mx+b). So, we have the original equation as follows:

 

-3x+5y=-10

 

Add 3x to each side in order to move the x's to the side opposite the y's. 

 

-3x+3x+5y=3x-10 --> 5y=3x+10 (Note that the 3x and the -3x cancel one another.)

 

From here, we divide each side by five, so the equation looks like...

 

5y/5=(3x+10)/5 --> y=(3/5)x+2 (The 5 in the 5y cancels with the five below, and the 5 on the right side is distributed between the two numbers in the sum in the parentheses.)

 

This is now in the y=mx+b form. 

 

We now choose two values for x, which we will then use to find points on the graph; say, x=0,1.

 

When x=0...

 

y=(3/5)(0)+2=2

 

And when x=1...

 

y=(3/5)(1)+2=3/5+10/5=13/5=2.6

 

From this, we know two points: (0,2) and (1,2.6). From here, simply draw the points on graph paper, put a line through them, and you have your graph.