Write an equation of a line through (5,6) and (-1,4)

Step-by-step explanation:

As we move from (-1, 4) to (5, 6), x increases by 6 and y increases by 2.

Thus, the slope of this line is m = rise / run = 2/6 = 1/3.

Starting from the slope-intercept form of the equation of a str. line,

y = mx + b

Substitute 6 for y and 5 for x, as well as 1/3 for m:

6 = (1/3)(5) + b.

Mult. both sides by 3, to eliminate fractions:

18 = 5 + 3b.  Then 3b must equal 13, and b = 13/3.

The desired equation is y = (1/3)x + 13/3.

Check:  Does the given point (-1, 4) satisfy this equation?

Is 4 = (1/3)(-1) + 13/3 true?

Is 4 = -1/3 + 13/3 true?  YES

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step-by-step explanation: