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

Answer 1

Julia Adams

#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#.

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Answer 2

Julia Adams

To write the equation of a line given two points, you first find the slope using the formula: ( m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ). Then, use one of the points and the slope in the point-slope form of a line equation: ( y - y_1 = m(x - x_1) ). Substituting the given points ( (-2, 1) ) and ( (-1, 3) ), the slope is ( m = \frac{{3 - 1}}{{-1 - (-2)}} = 2 ). Using point ( (-2, 1) ) and the slope ( m = 2 ), the equation is ( y - 1 = 2(x + 2) ) or ( y - 1 = 2x + 4 ). Simplifying yields ( y = 2x + 5 ), the equation of the line.

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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.