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(5,2) A line that passes through each given point and is parallel to y= -3x + 8

1 Answer

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Answer:


  • y = - 3x + 17

Explanation:

To find:-

  • The equation of the line passing through (5,2) and parallel to
    y = -3x+8

Answer:-

We are interested in finding out the equation of the line which is parallel to the given line. The equation of the given line is,


\longrightarrow y = -3x + 8 \\

The given line is in slope intercept form, the slope intercept form of the line is,

Slope intercept form :-


\longrightarrow \boxed{\boldsymbol{ y = mx + c }} \\

where ,


  • m is the slope .

  • c is the y-intercept .

On comparing, we have,


\longrightarrow y =\boxed{-3}x+8 \\

The slope is ,


\longrightarrow m = -3 \\

Now as , we know that the slopes of parallel lines are equal . Hence the slope of the line parallel to the given line, would be -3 . The given point to us is (5,2) ; so we can use the point slope form of the line to find out the equation. The point slope form of the line is,

Point slope form:-


\longrightarrow y - y_1 = m(x-x_1) \\

where ,


  • m is the slope .

  • (x_1,y_1) is the coordinate through which the line passes.

On substituting the respective values, we have;


\longrightarrow y - 2 = -3(x-5) \\

Simplify by opening the brackets , as ;


\longrightarrow y - 2 = -3x + 15\\

Add "2" on both the sides,


\longrightarrow y = -3x+15+2 \\

Add the constant terms ,


\longrightarrow \boxed{\boldsymbol{ y = -3x+17}}\\

This is the required equation of the line.

(5,2) A line that passes through each given point and is parallel to y= -3x + 8-example-1
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