Home > Algebra > Equations of Parallel Lines

How do you find the equation of the line parallel to #y=-5x+3# and passing through #(4,3)#?

Answer 1

Hazel Anglin

The equation is #y=-5x+23#

Parallel lines always have the same slope

The line parallel to #y=-5x+3# has a slope of -5, same as that line.

So far, the equation is #y=-5x+b#

Let's plug in (4, 3) to find the y-intercept (b)

#3=-5*4+b#

#3=-20+b#

#b=23#

The equation is #y=-5x+23#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Genesis Allen

To find the equation of a line parallel to ( y = -5x + 3 ) and passing through the point ( (4,3) ), you use the fact that parallel lines have the same slope. Since the given line has a slope of -5, the parallel line will also have a slope of -5. Therefore, the equation of the parallel line can be written in the form ( y = -5x + b ), where ( b ) is the y-intercept. To find ( b ), substitute the coordinates of the given point ( (4,3) ) into the equation and solve for ( b ).

So, ( 3 = -5(4) + b ). Solve for ( b ): ( b = 3 + 20 = 23 ).

Thus, the equation of the line parallel to ( y = -5x + 3 ) and passing through ( (4,3) ) is ( y = -5x + 23 ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.