Question

How do you write an equation for the line that is parallel to \[y=-5x+3\] and passes through (-6,3)?

Answer 1

Hint: This question is from the topic of geometry. In this question, we have to find the equation of the straight line using the given equation and point in the question. In solving this question, we will first find out the slope of line using the equation \[y=-5x+3\]. After that, we will use the slope of line and the point given in the question to find out the new equation of line using point- slope form.

Complete step-by-step solution:
Let us solve this question.
In this question, we have asked to find out the equation of line which is parallel to the equation of line \[y=-5x+3\] and passing through the point (-6,3).
We know that the general equation of line is \[y=mx+c\], where m is the slope of line.
So, we can say that the slope of the equation of line \[y=-5x+3\] is m=-5.
The point-slope formula of straight line is
\[\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)\], where \[\left( {{x}_{1}},{{y}_{1}} \right)\] is the point on the line.
So, having the slope as -5 and the point as (-6,3), we can write the equation of straight line using the point slope form as
\[\left( y-3 \right)=-5\left( x-\left( -6 \right) \right)\]
The above can also be written as
\[\Rightarrow y-3=-5\left( x+6 \right)\]
The above equation can also be written as
\[\Rightarrow y-3=-5x-30\]
The above equation can also be written as
\[\Rightarrow y=-5x-27\]
So, we can say that the equation of line which is parallel to \[y=-5x+3\] and passing through the point (-6,3) will be \[y=-5x-27\].
We can understand this from the following figure:

Note: We should have a better knowledge in the topic of geometry to solve this type of question easily. We should know about the point slope form. The formula for point-slope form is: \[\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)\], where m is the slope of line and \[\left( {{x}_{1}},{{y}_{1}} \right)\] is the point on the line. We should know about the slope intercept form of line. The slope intercept form of straight line is: \[y=mx+c\].