Question 201391: write an equation in standard form for a line passing through the pair of points.
(-2,0) and (4,-5)
possible answers:
2x-9y=-37
-5x-6y=10
-2x+9y=-37
5x-6y=10
Answer by algebrapro18(249)   (Show Source):
You can put this solution on YOUR website! write an equation in standard form for a line passing through the pair of points. (-2,0) and (4,-5).
Well from the points given we know that:
x1 = -2, y1= 0, x2 = 4, y2 = -5
First we need to find the slope of the line between those two points:
That uses the formula: m = y2-y1/x2-x1
So from above we get that: m = (-5-0)/ (4--2) = -5/6.
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.
Option 1: slope-intercept form:
we know that y = mx+b and we have a y, x, and m so we can solve for b.
y = mx+b
0 = -5/6(-2)+b
0 = 5/3+b
b = -5/3
or
y = mx+b
-5 = (-5/6)(4)+b
-5 = -10/3 + b
-5/3 = b
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.
y = -5/6x-5/3
6y = -5x - 10
5x + 6y = -10
-(5x+6y) = 10
-5x-6y = 10
Option 2: Point-Slope form
We know that y-y1=m(x-x1) so now we just plug in and simplify(not solve).
y - 0 = -5/6(x--2)
y = -5/6(x+2)
y = -5/6x-5/3
and now we just need to get into standard form.
y = -5/6x-5/3
6y = -5x - 10
5x + 6y = -10
-(5x+6y) = 10
-5x-6y = 10
Now I will leave it to you to check our answer, and you will see its right.
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