perpendicular line with equations and points

Question

1) Write an equation of the line that is: perpendicular to the line y=4x+1 and that passes through the point (2,3)

 

2) parallel to the line y-3x=5 and that passes through the point (-1,6) 

 

3) perpendicular to the line 2y-6x=9 and that passes through the point (-2,1)

 

4) parallel to the line y=4x+3 and that has the same y-intercept as the line y=5x-3

 

*please tell me what perpendicular mean and how you got your answer and how you set the equation up and why. Thank you! 

Answer 1

"perpendicular" means forming a 90 degree (or right angle) angle with.  So (1) equation of the line that is: perpendicular to the line y=4x+1 and that passes through the point (2,3) can be solved by finding the slope of the perpendicular line first.  The slope of a line perpendicular to another line is basically the negative reciprocal....So the slope of line will be -(1/4).  so now we have a portion of our equation....y= -(1/4)x+b.....Now we need to find the value of b.  We plug in the point (2,3) in for (x,y) to get 

 

3= -(1/4)*2 + b 

 

Solving for b yields 3 + (1/4)*2 = 3.5

 

So for # 1....our equation of the line perpendicular is y= -(1/4)x + 3.5

 

For # 2, do the same, but the parallel line will have the same slope.

 

For # 3, first solve for y, then find the slope of the line perpendicular, etc.....

 

For # 4, "parallel to the line y=4x+3 and that has the same y-intercept as the line y=5x-3" .  The y intercept of y=5x-3 is -3.  So since the parallel line has the same slope as 4x, then our parallel line is y=4x-3.

 

Hope this helps....I can't do every single one for you....you wouldn't learn anything.

 

Answer 2

Perpendicular lines have negative reciprocal slopes. For example, if a line has a slope of 2, then the line perpendicular to it has a slope of -1/2. Perpendicular lines intersect at a point and form 4 right angles. Think of a cross, or a lower-case t. Each of the lines written in your example are in the form y = mx + b, which is known as slope-intercept form. The m represents the slope of the line. The b represents the y-intercept. To find the equation of the line perpendicular to the given line, you can use the point-slope form of the equation of a line, which is y - y₀ = m(x - x₀), where m = slope and (x₀, y₀) = a point on the line. 

*Parallel lines have equal slopes.