How do you find the slope that is perpendicular to the line #4x+5y= -5#?

Question

Hazel Anglin · Accepted Answer

The slope of the line perpendicular to the line #4x+5y=-5# is #5/4#.

Let's start with the original equation: #4x+5y=-5# From here, we can manipulate the equation into the slope-intercept form. We first move the #4x# over to the right side by subtracting #4x# from both sides: #5y=-5-4x# Next, we divide both sides by #5# to isolate the #y# variable: #y=(-5-4x)/5# We then simplify the right portion of the equation: #y=-5/5-(4x)/5# And further simplification follows: #y=-1-(4x)/5# We then rearrange the entire equation to clearly show the equation in slope-intercept form: #y=-(4x)/5-1# Now that we have the equation in slope-intercept form, we can clearly see that #-4/5# is the slope here. From here, it is easy. The product of a slope and its perpendicular slope is always #-1#. (Proof: perpendicular lines have negative reciprocal slope) If we set #a# to be the perpendicular slope of #-4/5#, then #-4/5a=-1# Then, we can isolate #a# by dividing by #-4/5# on both sides and then simplifying the result: #a=(-1)/(-4/5)=-1*-5/4=5/4# Thus, the slope of the line perpendicular to the line #4x+5y=-5# is #5/4#.

Genesis Allen · Answer

The slope that is perpendicular to the line #4x + 5y = -5# is #5/4#.

The slope perpendicular to a line is the opposite reciprocal of the slope of the given line. For example, if the slope of a line is 2, the slope of a line perpendicular to the line with slope 2 must be #-1/2#. "Opposite" refers to the opposite sign (e.x. the opposite of #-5# is #5#), and "reciprocal" just means 1 over whatever you're given (e.x. the reciprocal of 20 is just #1/20#). Because in your case the line is in standard form (i.e. #ax + by = c#, such that #a# is a positive integer, and #b# and #c# are integers), the slope of the line is given by the equation: #m=-a/b#. Thus, the slope of the line is #-4/5#. You can also find the slope, #m#, by putting the equation into slope-intercept form (#y=mx+b#): 1. #4x + 5y = -5# 2. #5y = -4x - 5# 3. #y = -4/5x -1# 4. #m=-4/5# The slope of a line perpendicular to this line must be the opposite reciprocal, so #-(1/(-4/5)) = 5/4#. The slope that is perpendicular to the line #4x + 5y = -5# is #5/4#.

Eli Assouline · Answer

undefined To find the slope perpendicular to the line $4x + 5y = -5$, first, we need to rearrange the equation into slope-intercept form, $y = mx + b$, where $m$ represents the slope.

$4x + 5y = -5$ can be rewritten as $5y = -4x - 5$, then $y = -\frac{4}{5}x - 1$.

The slope of the given line is $-\frac{4}{5}$.

The slope of a line perpendicular to this line will be the negative reciprocal of $-\frac{4}{5}$.

So, the slope perpendicular to the given line is $\frac{5}{4}$.