Respuesta :
Answer:
Step-by-step explanation:
Use the point-slope formula.
y - y_1 = m(x - x_1) .... x_1 = 3 and y_1 = - 1
m is the slope to x - 3y = 9 because (lines are parallel )
calculate : m by equation x - 3y = 9 :
x = 3y +9
divid by : 3 1/3 x = y + 3
y = (1/3) x - 3 so : m = 1/3
an equation parallel to x - 3y = 9 that passes through the point ( 3, -1 ) is :
y +1 = (1/3)(x - 3)
The equation of the line parallel to x - 3y = 9 that passes through (3, -1) is x - 3y = 6
From the question,
We are to determine the equation of the line that is parallel to x - 3y = 9 and passes though the point (3, -1)
NOTE: The slope of two parallel lines as equal
Now, we will determine the slope of the line x - 3y = 9
We will rearrange the equation in the slope-intercept form of an equation of a straight line
The slope-intercept form of an equation of a straight line is
y = mx + c
Where m is the slope
and c is the y-intercept
Now, we will rearrange the equation x - 3y = 9, in the form
x - 3y = 9
This can be written as
x - 9 = 3y
That is,
[tex]3y = x - 9[/tex]
Dividing through by 3, we get
[tex]y = \frac{1}{3}x-3[/tex]
Comparing this to y = mx + c
∴ m = 1/3
That is, the slope of the line is 1/3
Since the two lines are parallel, that means the slope of the other line is also 1/3.
Now, we are to determine the equation of a line that has a slope of 1/3 and passing through the point (3, -1)
Using the point-slope form for determining the equation of a straight line
y - y₁ = m(x - x₁)
From the question,
x₁ = 3 and y₁ = -1
Putting these into the equation, we get
[tex]y - -1 = \frac{1}{3}(x-3)[/tex]
This becomes
[tex]y + 1 = \frac{1}{3}(x-3)[/tex]
Multiplying through by 3, we get
[tex]3(y+1) = (x-3)[/tex]
Clearing the brackets, we get
[tex]3y +3 = x-3[/tex]
Then
[tex]3 + 3 = x-3y[/tex]
[tex]6= x-3y[/tex]
That is,
[tex]x -3y = 6[/tex]
Hence, the equation of the line parallel to x - 3y = 9 that passes through (3, -1) is x - 3y = 6
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