Question

Create a linear equation for the following data:Ху-172-27-1710-26O y = 2x - 9O y = 5x - 2O y = -3x + 7O y = -3x + 4

Answer 1

Let's begin by identifying key information given to us:

`(x,y)=(-1,7),(2,-2),(7,-17),(10,-26)`

We will proceed to calculate the slope, we have:

`\begin{gathered} slope(m)=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ slope(m)=(-26-7)/(10-(-1))=(-33)/(10+1)=-(33)/(11) \\ slope(m)=-3 \\ \\ The\text{ equation becomes:} \\ y=-3x+b \end{gathered}`

We will use the point-slope equation to obtain the equation of this data. We have:

`\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(-1,7) \\ y-7=-3(x--1) \\ y-7=-3(x+1) \\ y-7=-3x-3 \\ \text{Add ''7'' to both sides, we have:} \\ y-7+7=-3x-3+7 \\ y=-3x+4 \\ \\ \therefore y=-3x+4 \end{gathered}`

Hence, the correct answer is y = -3x + 4