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
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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
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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