Gie\ven that the line which passes through A (2.5) and B (4.13) is parallel to the line which passes through the point M(2,5).
Consider points A (2.5) and B (4.13).
Recall the formula for the slope is
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ Substitute }\times x_1=2,x_2=4,y_1=5\text{ and }y_2=13,\text{ we get}[/tex][tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{13-5}{4-2}=\frac{8}{2}=4[/tex]We get the slope m=4.
We know the parallel lines have an equal slope.
The general form of the required line equation is
[tex]y=mx+b[/tex]Substitute m=4, we get
[tex]y=4x+b[/tex]This line is passing through point M(2,5).
Substitute x=2 and y=5 in y=4x+b, to find the value of b.
[tex]5=4(2)+b[/tex][tex]5=8+b[/tex]Subtracting 8 from both sides, we get
[tex]5-8=8+b-8[/tex][tex]-3=b[/tex]We get b=-3.
Substitute b=-3 in y=4x+b, we get
[tex]y=4x-3[/tex]Hence the required line equation is y=4x-3.
