The point slope of a linear equation is represented as: [tex]\mathbf{y - y_1 = m(x - x_1)}[/tex]
The steps calculate the equation are;
- [tex]\mathbf{y - 4 = -1(x - 2)}[/tex] or [tex]\mathbf{y - 7 = -1(x - -1)}[/tex]
- Followed by [tex]\mathbf{y = -x+6}[/tex]
The points are given as:
(-1,7) and (2,4)
Start by calculating the slope of the line
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
This gives
[tex]\mathbf{m = \frac{4-7}{2--1}}[/tex]
[tex]\mathbf{m = \frac{-3}{3}}[/tex]
[tex]\mathbf{m = -1}[/tex]
The equation is then calculated as:
[tex]\mathbf{y - y_1 = m(x - x_1)}[/tex]
This gives:
[tex]\mathbf{y - 7 = -1(x - -1)}[/tex]
[tex]\mathbf{y - 7 = -1(x+1)}[/tex]
[tex]\mathbf{y - 7 = -x-1}[/tex]
Collect like terms
[tex]\mathbf{y = -x-1 + 7}[/tex]
[tex]\mathbf{y = -x+6}[/tex]
Hence, the equation of the line is:
[tex]\mathbf{y = -x+6}[/tex]
Read more about point-slope form method at:
https://brainly.com/question/19214360
