Question

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 change? Use examples of your own to explain the process

Answer 1

Step-by-step 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.

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

$\text{Slope}=\frac{6-0}{3-0} =\frac{6}{3} =2$

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

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

$y=2x-6+6$

$y=2x-6+6$

$y=2x$

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 $y=-2*x+4$.

Answer 2

Answer:

find the domain

Step-by-step explanation: