How do you write an equation of the line with f(-2)=1 and f(-1)=3?

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Answer 1 · 2015-07-15T15:41:04

#y=2x+5# in slope-intercept form and #2x-y+5=0# in standard form.

The slope of the line is

#\frac{\mbox{rise}}{\mbox{run}}=\frac{\Delta y}{\Delta x}=\frac{f(-1)-f(-2)}{-1-(-2)}=\frac{3-1}{-1+2}=2/1=2#

Therefore, the equation of the line can be written (in point-slope form) as

#y=2(x-(-2))+1=2(x+2)+1#.

Using the distributive property and simplifying gives the slope-intercept form

#y=2x+5#.

Rearranging gives the standard form

#2x-y+5=0#.