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The x-intercept of a line with a gradient (slope) of #5/6# is #-3#. What is the equation of the line in slope-intercept form?

Answer 1

Hazel Anglin

The equation of the line is:

#y = 5/6x+15/6#

We often work with the y-intercept, but the x-intercept is less common. Still not too difficult, though.

We can write the equation of a line in standard form as:

#y=mx+c#

where #m# is the slope and #c# is the y-intercept.

We find the y-intercept by setting #x=0#, since the y-axis is the line #x=0#.

Let's see whether turning that around will work: let's set #y=0#, since the x-axis is the line #y=0#, then the value of #x# has been given to us as #-3#:

#y=mx+c#

#0=5/6(-3)+c#

Rearranging, we get:

#c=-5/6(-3)=15/6#

The overall equation of the line, then, is:

#y = 5/6x+15/6#

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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.