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what is the equation of a line passing through the point (6,1) and parallel to the line whose equation is 3x-2y= 4

User Gaitat
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1 Answer

3 votes

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

User Dave Templin
by
7.4k points