I found three points of the equation
x-2y=b which were (4, -2) (0,-4)(-4,-6)
But the question further asks to convert the equation of the new line to standard form ax+by=c.
I'm so confused. Can anyone please help?
well, your equation, which is already in standard form, just needs a value for b.
just plug in a point
x-2y=b
4-2(-2) = b
so, b=8
x-2y=8
which is standard form with
a=1
b=-2
c=8
I get it! I thought I would have to use all the points
Sure! I'd be happy to help you convert the equation of the line from the given points to standard form.
To convert the equation of a line to standard form (ax + by = c), we want to eliminate any fractions or decimals and have whole number coefficients for both x and y. Here's how you can do it step by step:
Step 1: Start with the given points and equation
Points:
(4, -2), (0, -4), (-4, -6)
Equation:
x - 2y = b
Step 2: Choose any two of the given points and substitute their x and y values into the equation.
Let's choose the points (4, -2) and (0, -4).
Substitute the values of the first point (4, -2):
4 - 2(-2) = b
4 + 4 = b
b = 8
Substitute the values of the second point (0, -4):
0 - 2(-4) = b
0 + 8 = b
b = 8 (same value as before)
So we have found that b is equal to 8 using both points.
Step 3: Now substitute the value of b back into the equation.
x - 2y = 8
Step 4: Rearrange the equation to match the standard form (ax + by = c).
To eliminate the coefficient of -2y, we can multiply both sides of the equation by -1.
-1(x - 2y) = -1(8)
-x + 2y = -8
Now, let's multiply both sides of the equation by -1 again to have positive coefficients for x.
(-1)(-x + 2y) = (-1)(-8)
x - 2y = 8
And voila! Now the equation x - 2y = 8 is in standard form (ax + by = c), where a = 1, b = -2, and c = 8.
I hope this explanation helps you understand how to convert an equation to standard form. Let me know if you have any further questions!