How do you find the slope and intercept of #8x + 4y = -96#?

2 Answers
May 6, 2016

Answer:

#m=-2# ,x-intercept=-12
y-intercept=-24

Explanation:

#8x+4y=-96#
Dividing both sides by 4 we have
#2x+y=-24#
#=>y=-2x-24#
Comparing this with slope imtercept form #y=mx+c# .where m is the slope c is intercept from y-axis
Slope=-2 and y-intercept#c=-24#

x-intercept can be had by putting y=0 in the equation

#0=-2x-24=>x=-12#
So x-intercept=-12

May 6, 2016

Answer:

Slope = #-2#

#y#-intercept is #-24# and the point is #(0,-24)#

#x#-intercept is #-12# and the point is #(-12,0)#

Explanation:

We can see that 4 is a factor common to all the terms in the given equation.

#4xx2x + 4y = -24 xx 4#

#=> 4(2x+y) = -24 xx 4#

Divide both sides by 4:

#[4(2x+y)]/4 = (-24 xx 4)/4#

#=> 2x+y = -24#

This can also be written as

#y = -2x-24#

First, we will find the slope

The equation of a line is of the form #color(red)(y=mx+c)#

Where, #m# is the slope of the line and #c# is the #y#-intercept.

Comparing #y=mx+c# to the given equation, #y = -2x-24#

#m=-2# and #c=-24#

#=># Slope #= -2# and #y#-intercept #= -24#

The #y#-intercept is the point where the line cuts the #y#-axis. i.e. the point when #x=0#.

Therefore, the #y#-intercept is the point #(0,-24)#.

Next, we find the intercepts

We have already found the #y#-intercept above.

The #x#-intercept is the point where the line cuts the #x#-axis. i.e. to find the point when #y=0#.

Pretty simple.

Here is a step-by-step to work out the #x#-intercept.

enter image source here

The #x#-intercept is the point #(-12,0)#.