Question

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Answer 1

`\boxed{\large\sf y = 3x - 5}`

Explanation:

Here we are given a equation which is ,

`\longrightarrow y = 3x + 6`

We need to find out the equation of the line which is parallel to the given line and passes through the given point .

• And as we know that the slope of two parallel lines are equal .

On comparing the given equation with slope intercept form (y = mx + c )of the line , we have ,

`\longrightarrow m = 3`

Therefore the slope of the parallel line will be ,

`\longrightarrow m_(||)= 3`

Now we can use the point slope form of the line which is ,

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

Substitute ,

`\longrightarrow y - 7 = 3 ( x -4)\\\\\longrightarrow y -7 = 3x -12 \\\\\longrightarrow y = 3x -12+7\\\\\longrightarrow y = 3x -5`

This is the required answer .