Answer:
c. [tex]y+1=-\frac{1}{4} (x-1)[/tex]
Step-by-step explanation:
Hi there!
We are given the points (1, -1) and (5, -2)
We want to find the equation of that line using those points, in point-slope form
Point-slope form is written as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point
First, let's find the slope of the line
The formula for the slope (m) calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We already have everything we need to find the slope, but let's label the values of the points to avoid any confusion when calculating.
[tex]x_1=1\\y_1=-1\\x_2=5\\y_2=-2[/tex]
Now substitute:
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-2--1}{5-1}[/tex]
Subtract
m=[tex]\frac{-2+1}{5-1}[/tex]
m=[tex]\frac{-1}{4}[/tex]
The slope of the line is -1/4
Now substitute this into the formula to find point-slope form (remember that this is [tex]y-y_1=m(x-x_1)[/tex], and that m is the slope value)
Therefore:
[tex]y-y_1=-\frac{1}{4} (x-x_1)[/tex]
Now, let's substitute the values of [tex]x_1[/tex] and [tex]y_1[/tex], which we found earlier (which are 1 and -1 respectively) into the equation
[tex]y--1=-\frac{1}{4} (x-1)[/tex]
Simplify
[tex]y+1=-\frac{1}{4} (x-1)[/tex]
This equation matches option c, which is the answer.
Hope this helps!
