Answer:
y = 5/6x - 2
Explanation:
Pre-Solving
We are given that a line is perpendicular to 6x+5y=10, and passes through the point (6,3). We want to write the equation of this line.
Solving
Slope
Perpendicular lines have slopes that multiply to -1, so let's start by finding the slope of 6x+5y=10.
This line is currently in standard form, which is ax+by=c, where a, b, and c are free integer coefficients.
The slope (m) can be found using the formula -a/b.
We can label the values of the coefficients to help us:
a = 6
b = 5
c = 10
Now, substitute the values into the formula.
m = -a/b = -6/5
So, the slope of 6x + 5y = 10 is -6/5, but it's not the slope of the line we want to find (recall we want to find the perpendicular line).
To find the slope of the line we want to find, we can use this formula:
-6/5m = -1
Multiply both sides by -5/6.
m = 5/6
Equation of the line
We can write the equation of this line in slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.
Since we already know the slope of this line, we can immediately plug it into the equation.
y = 5/6x + b
We need to find b now.
As the equation passes through the point (6,3), we can use its values to help solve for b.
Substitute 6 as x and 3 as y.
3 = 5/6(6) + b
Multiply.
3 = 5 + b
Subtract 5 from both sides.
-2 = b
Substitute -2 as b.
y = 5/6x - 2