Question

graph the equation and find the y-intercept.

2y+5x=-6

My question is do I add -5x to both sides first?? how do I start this problem?

Answer 1

When you have an equation with just x and y terms, you're looking at a straight line.

One way to approach is it, as you say, to add -5 to both sides, and then divide across by 2, so that the LHS just contains y on its own. Then you have it in the form y = mx + c, and you can just read off the y-intercept as c.

Another way to find the y-intercept is to set x=0, and see what you're left with:

2y+5x=-6
2y+0 = -6
y=-3

So the point (0,-3) is on the line, and is the y-intercept.

You also want to graph it. Since it's a straight line, you just need two points, then draw the line with a ruler.
Let's get the x-intercept as our other point:

2y+5x=-6
0+5x=-6
x=-6/5

So (-6/5,0) is tyhe x-intercept, and the second point we need for drawing the line.

Answer 2

Oops, typo. In case you're confused, I meant "One way to approach it is, as you say, to add -5x to both sides..."