We must find the equation of the line that passes through points A = (-7,-6) and B = (-1,0).
The general slope-intercept equation of a line is:
[tex]y=m\cdot x+b,[/tex]
where the b is the y-intercept and m is the slope of the line.
1) We compute the slope using the following formula:
[tex]m=\frac{y_B-y_A}{x_B-x_A_{}}_{}_{},[/tex]
where (xA,yA) and (xB,yB) are the coordinates of the points A and B, respectively.
Replacing the coordinates of the points of the problem, we find that:
[tex]m=\frac{0-(-6)}{-1-(-7)}=1.[/tex]
2) To compute the y-intercept b, we replace the value of m = 1 and the coordinates of one of the points (B for example) in the general equation of the line, and then we solve for b:
[tex]\begin{gathered} y_B=m\cdot x_B+b, \\ 0=1\cdot(-1)+b, \\ b=1. \end{gathered}[/tex]
Replacing the values m = 1 and b = 1 in the equation of the line, we find that:
[tex]y=x+1[/tex]
Answer
The equation of the line is:
[tex]y=x+1[/tex]
