First thing to remember is that y=mx+b, so change the equation that you have into that format (much easier to work with)
6y = -5x + 3 --> y = (-5/6)x + 3/6 --> y = (-5/6)x + 1/2
After we have this format down, we can see that the slope of the original function is -5/6.
For a line that is perpendicular to this line, the slope is the inverse opposite. So, for our case it is 6/5.
[ -5/6 * -1] --> 5/6 and then you flip it to get 6/5.
This gives us an equation of y = (6/5)X + b, the intercept is going to be different because we have an entirely new line.
We can then plug in our new points (4,3) and we have the function:
3 = (6/5) * 4 + b
Then we can multiply this out and get 3 = (24/5) + b
We want the "b" all by itself, so we can subtract the (24/5) from the right side and have:
3 - (24/5) = b, converting this to a number we can see that it is 15/5 - 24/5, which comes out to:
- 9/5 = b, or -1.8 = b, in decimal form.
So our new line is going to be:
y = (6/5)x - 9/5 or y = (6/5)x - 1.8
6y = -5x + 3 --> y = (-5/6)x + 3/6 --> y = (-5/6)x + 1/2
After we have this format down, we can see that the slope of the original function is -5/6.
For a line that is perpendicular to this line, the slope is the inverse opposite. So, for our case it is 6/5.
[ -5/6 * -1] --> 5/6 and then you flip it to get 6/5.
This gives us an equation of y = (6/5)X + b, the intercept is going to be different because we have an entirely new line.
We can then plug in our new points (4,3) and we have the function:
3 = (6/5) * 4 + b
Then we can multiply this out and get 3 = (24/5) + b
We want the "b" all by itself, so we can subtract the (24/5) from the right side and have:
3 - (24/5) = b, converting this to a number we can see that it is 15/5 - 24/5, which comes out to:
- 9/5 = b, or -1.8 = b, in decimal form.
So our new line is going to be:
y = (6/5)x - 9/5 or y = (6/5)x - 1.8
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any line passing through (h, k) and perpendicular to line ax + by + c = 0 is given by
b(x -- h) -- a(y -- k) = 0
line passing through (4, 3) and perpendicular to line 5x + 6y = 3 is given by
6(x -- 4) -- 5(y -- 3) = 0 OR 6x -- 5y = 9 ANSWER
b(x -- h) -- a(y -- k) = 0
line passing through (4, 3) and perpendicular to line 5x + 6y = 3 is given by
6(x -- 4) -- 5(y -- 3) = 0 OR 6x -- 5y = 9 ANSWER
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6x-5y = c , and plug (4,3) to find c