Question 201391
write an equation in standard form for a line passing through the pair of points. (-2,0) and (4,-5).<br>

Well from the points given we know that:<br>

x1 = -2, y1= 0, x2 = 4, y2 = -5<br>

First we need to find the slope of the line between those two points:
That uses the formula: m = y2-y1/x2-x1<br>

So from above we get that: m = (-5-0)/ (4--2) = -5/6.<br>

Now we can continue in 1 of two ways. Either we can plug in to the slope-intercept form and solve for b and then get into standard form, or we can use the point slope formula and get it in standard form.<br>

Option 1: slope-intercept form:<br>

we know that y = mx+b and we have a y, x, and m so we can solve for b.<br>

y = mx+b                        
0 = -5/6(-2)+b                 
0 = 5/3+b                       
b = -5/3<br>                       

or<br>

y = mx+b
-5 = (-5/6)(4)+b
-5 = -10/3 + b
-5/3 = b<br>

so now we know that y = -5/6x-5/3.  To get it into standard form we need to get the x and the y isolated on the same side.  <br>

y = -5/6x-5/3
6y = -5x - 10
5x + 6y = -10 
-(5x+6y) = 10
-5x-6y = 10<br>

Option 2: Point-Slope form
We know that y-y1=m(x-x1) so now we just plug in and simplify(not solve).<br>

y - 0 = -5/6(x--2)
y = -5/6(x+2)
y = -5/6x-5/3<br>

and now we just need to get into standard form.<br>

y = -5/6x-5/3
6y = -5x - 10
5x + 6y = -10 
-(5x+6y) = 10
-5x-6y = 10<br>

Now I will leave it to you to check our answer, and you will see its right.