Given:
The coordinates are:
Find-:
The equation of a line
Explanation-:
The general equation is:
[tex]y=mx+c[/tex]
Where,
[tex]\begin{gathered} m=\text{ Slope} \\ \\ (x,y)=\text{ Coordintes of line} \\ \\ c=\text{ y-intercept} \end{gathered}[/tex]
The formula of the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Choose any two points from the chart is:
[tex]\begin{gathered} (x_1,y_1)=(-1,-5) \\ \\ (x_2,y_2)=(0,-2) \end{gathered}[/tex]
Then the slope is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{-2-(-5)}{0-(-1)} \\ \\ m=\frac{-2+5}{0+1} \\ \\ m=\frac{3}{1} \\ \\ m=3 \end{gathered}[/tex]
If the slope of the line is 3, then the equation becomes:
[tex]\begin{gathered} y=mx+c \\ \\ y=3x+c \end{gathered}[/tex]
The value of "c" is:
Choose any one point.
[tex](x,y)=(0,-2)[/tex]
The value of "c" is:
[tex]\begin{gathered} y=3x+c \\ \\ (x,y)=(0,-2) \\ \\ -2=3(0)+c \\ \\ -2=0+c \\ \\ c=-2 \end{gathered}[/tex]
The equation of line is:
[tex]\begin{gathered} y=mx+c \\ \\ y=3x+(-2) \\ \\ y=3x-2 \end{gathered}[/tex]
The equation of line is y = 3x-2
