When given 2 data points, how would you use this information to create a linear equation? How would you create a linear equation if you were given an initial value and a rate of…

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asked Oct 3, 2019 162k views

1 Answer

Sharleen · Answer 1 · 2019-10-09T10:22:11+0000

Explanation:

A. When we are given two points we can find a linear equation by finding slope of the line and substituting it in point-slope form of equations.

Let (0,0) and (3,6) be two data points. Now we will find slope from these points.

$\text{Slope}=\frac{\text{Rise}}{\text{Run}}$

$\text{Slope}=(6-0)/(3-0) =(6)/(3) =2$

Now we will substitute our values in point-slope form of linear equations.
(y-y_1)=m(x-x_1)

(y-6)=2(x-3)

y=2x-6+6

y=2x

Therefore, our resulted linear equation will be
y=2*x

B. We will substitute the rate of change (slope) and initial value (y-intercept) into slope-intercept form of line to get the desired equation.

Let 4 be our initial value and -2 be our rate of change then,
4=-2*x+b

Substituting x=0 we will get value for b that is our y-intercept.

4=-2*0+b

4=b

y=-2*x+4

Therefore, our equation for line will be
y=-2*x+4 .