The general form of the equation of a line is given by;
[tex]y=mx+b[/tex]where m is the slope of the line and b is the y-intercept.
You have the following equation of a line:
[tex]y=2x-5[/tex]a) By comparing the previous equation with the general form of the equation of a line, you can notice that the slope of the line is m = 2.
b) Any equation of a line with the same slope will be parallel to the line
y = 2x - 5.
c) You use the following formula for the slope of a line:
[tex]m=\frac{y-y_1}{x-x_1}[/tex]where (x1,y1) is a point of the line.
If you replace the given point (-2 , -1) in the previous equation, if you also replace the value of m and solve for y, you obtain:
[tex]\begin{gathered} m=\frac{y-(-1)}{x-(-2)} \\ m=\frac{y+1}{x+2} \\ m(x+2)=y+1 \\ m(x+2)-1=y \\ mx+2m-1=y \\ 2x+2(2)-1=y \\ 2x+4-1=y \\ 2x+3=y \end{gathered}[/tex]Which is the same as:
y = 2x + 3
Hence, the equation y = 2x + 3 is a line parallel to the line y = 2x - 5 and passes trough the point (-2,-1)
