How do you find the slope and intercept of # 5-x = y/3#?

2 Answers
Apr 4, 2016

Answer:

The slope is 3 and the y-intercept is -15.

Explanation:

To solve this problem, we must first put the original equation in slope-intercept form. To do this, we'll multiply each side by 3 to get #15-3x=y#, or #y=3x-15#. From here, it's easy to find the slope and intercept. Since slope-intercept form is #y=mx+b#, where m is the slope and b is the y-intercept, the slope is 3 and the y-intercept is -15.

Apr 4, 2016

Answer:

#color(blue)(x_("intercept")=5)#

#color(blue)(y_("intercept")=15)#

#color(blue)("The slope is "-3)#

Explanation:

Given:#" "5-x=y/3#

Multiply both sides by 3

#3(5-x)=yxx3/3#

But #3/3 =1#

#y=3(5-x)#

Multiply everything inside the brackets by 3

#y=15-3x#

The slope is the number (coefficient) in front of the #x#

#color(blue)("So the slope is "-3)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This means that as you read from left to right: for every 1 along you go down by 3. If the slope had been +3 that would mean you go up by 3 for every 1 along.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine y-intercept")#

The #y_("intercept")# is the constant of 15 from #y=-3x+15#

#color(blue)(y_("intercept")=15)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine x-intercept")#

#color(brown)("Calculation shown in a lot of detail")#
#color(brown)("Normally a lot od steps would be skipped")#

The #x_("intercept")# is when y=0

#0=-3x+15#

Subtract 15 from both sides

#-15=-3x+0#

divide both sides by 3

#-15/3=x xx -3/3#

#-5=-x#

Multiply everything by (-1)

#5=x#

#x=5#

#color(blue)(x_("intercept")=5)#