Answer:
y = 3/2x - 8
Explanation:
Pre-Solving
We are given the point (6, 1).
We want to find the equation of the line that passes through (6,1) and is parallel to 3x-2y=4.
Parallel lines have the same slope.
Solving
Slope
Let's first find the slope of 3x-2y=4.
It is currently in standard form, which is ax+by=c, where a, b, and c are free integer coefficients.
To find the slope, we can do -a/b.
We can label the values of the coefficients:
a = 3
b = -2
c=4
Now, substitute:
-a/b = -(3)/-2= 3/2
So, the slope of the line is 3/2.
It is also the slope of the line we want to find.
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 y-intercept.
So, let's substitute 3/2 for m.
y = 3/2x + b
We need to find b now.
y-intercept
Since the point passes through the point (6,1), we can use its values to help solve for b.
Substitute 6 as x and 1 as y.
1 = 3/2(6) + b
Multiply
1 = 9 + b
Subtract 9 from both sides.
-8 = b
Substitute -8 as b in the equation.
y = 3/2x - 8