Respuesta :
Answer:
Using point (-21, -22): y = (6/7)x - 4
Using point (-14, -16): y = (6/7)x - 4
Explanation:
The point-slope form of a line's equation is:
[tex]y-y_1=m(x-x_1)[/tex]Where (x₁, y₁) is a point in the line and m is the slope.
The slope of a line can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x₁, y₁) and (x₂, y₂) are two points in the line. So, replacing (x₁, y₁) by (-21, -22) and (x₂, y₂) by (-14, -16), we get that the slope of the line is:
[tex]m=\frac{-16-(-22)}{-14-(-21)}=\frac{-16+22}{-14+21}=\frac{6}{7}[/tex]Now, using the point (-21, -22), we get that the equation of the line is:
[tex]\begin{gathered} y-(-22)=\frac{6}{7}(x-(-21)) \\ y+22=\frac{6}{7}(x+21) \end{gathered}[/tex]Then, we can simplify the equation as:
[tex]\begin{gathered} y+22=\frac{6}{7}(x)+\frac{6}{7}(21) \\ y+22=\frac{6}{7}x+18 \\ y+22-22=\frac{6}{7}x+18-22 \\ y=\frac{6}{7}x-4 \end{gathered}[/tex]On the other hand, using the point (-14, -16), the equation of the line is:
[tex]\begin{gathered} y-(-16)=\frac{6}{7}(x-(-14)) \\ y+16=\frac{6}{7}(x+14) \end{gathered}[/tex]Simplifying, we get:
[tex]\begin{gathered} y+16=\frac{6}{7}x+\frac{6}{7}(14) \\ y+16=\frac{6}{7}x+12 \\ y+16-16=\frac{6}{7}x+12-16 \\ y=\frac{6}{7}x-4 \end{gathered}[/tex]So, the answers are:
Using point (-21, -22): y = (6/7)x - 4
Using point (-14, -16): y = (6/7)x - 4
