How do you find the x and y intercept of #y = 3x – 8#?

Question

Eva Abramson · Accepted Answer

Solution provided in extreme detail.

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

#y_("intercept")= -8# #color(blue)("Determin the y intercept")# Consider the standardised format of #y=mx+c# #color(blue)(y_("intercept")=c = -8)# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Determine the x intercept")# The x-intercept is when y = 0 because that is the value of y where the x-axis crosses it Set y = 0 giving:#" "0=3x-8# Add #color(red)(8)# to both sides #color(green)(0color(red)(+8)" "=" "3x-8color(red)(+8))# But #-8+8=0# giving: #8=3x# Divide both sides by #color(red)(3)# #color(green)(8/(color(red)(3))=3/(color(red)(3))x)# But #3/3=1 and 1xx x = x# giving: #8/3=x# Write as #color(blue)(x_("intercept")=8/3)#

Jameson Allen · Answer

undefined To find the x-intercept, set y = 0 and solve for x. To find the y-intercept, set x = 0 and solve for y.

For the x-intercept:
0 = 3x - 8
3x = 8
x = 8/3

For the y-intercept:
y = 3(0) - 8
y = -8

Therefore, the x-intercept is (8/3, 0) and the y-intercept is (0, -8).