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How do you find the x and y intercept of #3x − y = 5 #?

Answer 1

Nathan Axel

#x_("intercept")=5/3#

#y_("intercept")=-5#

#color(blue)("Determine "y_("intercept"))#

The y-axis crosses the x-axis at #x=0# so to find the y-intercept substitute #x=0# into the equation

#color(brown)(3x-y=5)color(blue)(" "->" "3(0)-y=5#

But #3xx0=0# giving

#-y=5#

Multiply both sides by #(-1)#

#(-y)xx(-1)=5xx(-1)#

#y=-5#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Determine "x_("intercept"))#

The x-axis crosses the y-axis at #y=0# so to find the x-intercept substitute #y=0# into the equation

#color(brown)(3x-y=5)color(blue)(" "->" "3x-0=5#

#color(brown)(3x=5)#

Divide both sides by #color(blue)(3)#

#color(brown)(3/(color(blue)(3)) xx x=5/(color(blue)(3))#

But #3/3=1#

#x=5/3#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)(3x-y=5)" "->" "color(blue)(y=3x-5)#

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Answer 2

Savannah Anderson

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 equation 3x - y = 5, the x-intercept is (5/3, 0) and the y-intercept is (0, -5).

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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.