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Indicate the equation of the given line in standard form.

The line that contains the point Q( 1, -2) and is parallel to the line whose equation is

y - 4 = 2/3 (x - 3)

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User Andreas Noack
by
3.5k points

1 Answer

13 votes
13 votes

Answer:

The equation of the line is;

3y = 2x-8

Explanation:

Firstly, we need the to get the slope of the given line

To do this, we will write the equation of the line in the standard form

the standard form

is;

y = mx + b

where m is the slope and b is the y-intercept

y -4 = 2/3(x-3)

y -4 = 2x/3 - 2

y = 2x/3 -2 + 4

y = 2x/3 + 2

with respect to the given equation, the slope of the line is 2/3

Mathematically, when two lines are parallel, the slopes of the line are equal

So now, we want to find the equation of the line that has a slope of 2/3 and passes through the point (1,-2)

so;

y = 2x/3 + b

So substitute the values of (1,-2)

1 for x and -2 for y

-2 = 2/3(1) + b

-2 = 2/3 + b

b = -2 - 2/3

b = (-6-2)/3 = -8/3

So the equation of that line is;

y = 2/3x - 8/3

Multiply through by 3

3y = 2x - 8

User Zorida
by
2.9k points
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