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What are the intercepts of the line #y = 1/2x-3#?

Answer 1

x-intercept #= 6#
y-intercept #=-3#

The x-intercept is the point where the graph crosses the X-axis; for all point on the X-axis, #y=0# Substituting #0# for #y# in #y =1/2x-3# we get #color(white)("XXX")0=1/2x-3#

#rarrcolor(white)("XXX")1/2x = 3#

#rarrcolor(white)("XXX")x=6#

Similarly, the y-intercept is the point where the graph crosses the Y-axis; and for all point on the Y-axi, #x=0# Substituting #0# for #x# in #y=1/2x-3# we get #color(white)("XXX")y =1/2*(0) -3#

#rarrcolor(white)("XXX")y=-3#

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Answer 2

Eva Adamson

You set #x# and #y# to #=0# in turn

#y#-intercept is when #x=0# Then #y=-3->(0,-3)#

#x#-intercept is when #y=0# #1/2 x-3=0->1/2 x=3->x=6->(6,0)# graph{0.5x-3 [-6.92, 13.08, -5.76, 4.24]}

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Answer 3

Jameson Allen

To find the intercepts of the line (y = \frac{1}{2}x - 3), you can set (x) or (y) equal to zero and solve for the other variable.

To find the (y)-intercept, set (x = 0) and solve for (y):

(y = \frac{1}{2}(0) - 3)
(y = -3)

So, the (y)-intercept is ((-3, 0)).

To find the (x)-intercept, set (y = 0) and solve for (x):

(0 = \frac{1}{2}x - 3)
(3 = \frac{1}{2}x)
(6 = x)

So, the (x)-intercept is ((6, 0)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.