Answer : The slope of the line and equation of the line is, [tex]\frac{-1}{2}[/tex] and [tex]y=\frac{-1}{2}x+8[/tex] respectively.
Step-by-step explanation :
The general form for the formation of a linear equation is:
[tex](y-y_1)=m\times (x-x_1)[/tex] .............(1)
where,
x and y are the coordinates of x-axis and y-axis respectively.
m is slope of line.
First we have to calculate the slope of line.
Formula used :
[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
Here,
[tex](x_1,y_1)=(2,7)[/tex] and [tex](x_2,y_2)=(4,6)[/tex]
[tex]m=\frac{(6-7)}{4-2)}[/tex]
[tex]m=\frac{-1}{2}[/tex]
Now put the value of slope in equation 1, we get the linear equation.
[tex](y-y_1)=m\times (x-x_1)[/tex]
[tex](y-7)=\frac{-1}{2}\times (x-2)[/tex]
[tex]y-7=\frac{-1}{2}x+1[/tex]
[tex]y=\frac{-1}{2}x+1+7[/tex]
[tex]y=\frac{-1}{2}x+8[/tex]
Thus, the slope of the line and equation of the line is, [tex]\frac{-1}{2}[/tex] and [tex]y=\frac{-1}{2}x+8[/tex] respectively.
