What is the equation of the line passing through the point (4, 6) and parallel to the line y= 1/4x + 4?

Emmett Bradley

Emmett Bradley

Answered question

2023-02-15

What is the equation of the line passing through the point (4, 6) and parallel to the line y= 1/4x + 4?

Answer & Explanation

Libby Fernandez

Libby Fernandez

Beginner2023-02-16Added 5 answers

To draw a line you either need twoof its points, or one of its points and its slope. Let's use this second approach.
We already have the point ( 4 , 6 ) . We derive the slope from the parallel line.
To begin with, two lines are only considered parallel if and when they have the same slope. The slope of our line will be equal to that of the given line.
Secondly, to derive the slope from a line, we write its equation in the y = m x + q form. The slope will be the number m
In this case, the line is already in this form, so we immediately see that the slope is 1 4
Recapping: we need a line passing through ( 4 , 6 ) and having slope 1 4 .
The formula that gives the line equation is the following:
y - y 0 = m ( x - x 0 )
where ( x 0 , y 0 ) is the known point, and m is the slope. Let's plug our values:
y - 6 = 1 4 ( x - 4 )
Expanding the right hand side:
y - 6 = 1 4 x - 1
Add 6 to both sides:
y = 1 4 x - 1 + 6
So, the response is
y = 1 4 x + 5
Rose Weaver

Rose Weaver

Beginner2023-02-17Added 1 answers

Parallel lines have the same slope, so the missing equation must have 1 4 as its slope.
Following the given, substituting 4 as x yields y = 6 , so as a shortcut, one can form the equation: 6 = 1 4 ( 4 ) + b to find b
This becomes: 6 = 1 + b , where b = 5
The final response is the slope-intercept form substitution:
y = 1 4 x + 5

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