How do you find the x and y intercept of #9x + 8y = −24#?

1 Answer
Jul 11, 2016

Answer:

#y_("intercept") = -3#

#x_("intercept") = - 8/3#

Explanation:

Convert the formula into the standard form of #y=mx+c# for a straight line graph.

Subtract #color(blue)(9x)# from both sides

#color(brown)(9xcolor(blue)(-9x)+8y=-24color(blue)(-9x))#

#8y=-9x-24#

Divide both sides by #color(blue)(8)#

#color(brown)(8/(color(blue)(8))xxy=-9/(color(blue)(8))x-24/(color(blue)(8)))#

But #8/8=1" and "24/8 =3# giving

#y=-9/8x-3#
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine y intercept")#

The line crosses the y-axis at #x=0# so by substitution

#color(brown)(y=-9/8x-3)color(blue)(" "->" "y=-9/8(0)-3#

#y_("intercept") = -3#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine x intercept")#

The line crosses the x-axis at #y=0# so by substitution

#color(brown)(y=-9/8x-3)color(blue)(" "->" "0=-9/8x-3#

#9/8x=-3#

#x=cancel((-3))^(-1)xx8/(cancel(9)^3)" " =" "- 8/3" " =" " -2 2/3#

#x_("intercept") = - 8/3#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Tony B