Question

32. Find the equation of the line that matches thefollowing data table:Xy491661A. y = -x + 10B. y = x +9C. y = -3x + 3D. y = 3x + 9

Answer 1

A. y = -1/4x + 10

Step-by-step explanation

We have to find the equation of the line in slope-intercept form,

`y=mx+b`

Where m is the slope and b is the y-intercept.

The slope of a line passing through points (x₁, y₁) and (x₂, y₂) is,

`m=(y_1-y_2)/(x_1-x_2)`

In this case, only two points are given, so the slope of the line is,

`m=(6-9)/(16-4)=(-3)/(12)=-(1)/(4)`

So, for now, the equation is,

`y=-(1)/(4)x+b`

To find the y-intercept, b, replace x and y with one of the points,

`9=-(1)/(4)(4)+b`

And solve for b,

`9=-1+b\text{ }\Rightarrow\text{ }b=9+1=10`

Hence, the equation of the line is y = -1/4x + 10.