Question

Vladimir says that the equation of the line that passes through the points (-5 -3) and (10 9) is y 4/5x+1. robyn says that the line through the points (-10 -7) and(-15 -11). who is correct

Answer 1

The equation of a line is given by:

`y-y_1=m(x-x_1)`

where m is the slope and (x1,y1) is a point on the line.

The slope is given by:

`m=(y_2-y_1)/(x_2-x_1)`

The slope of the line that passes through the points (-5,-3) and (10,9) is:

`\begin{gathered} m=(9-(-3))/(10-(-5)) \\ =(9+3)/(10+5) \\ =(12)/(15) \\ =(4)/(5) \end{gathered}`

Then, the equation of the line passes that passes through the points (-5,-3) and (10,9) is:

`\begin{gathered} y-9=(4)/(5)(x-10) \\ y-9=(4)/(5)x-(40)/(5) \\ y-9=(4)/(5)x-8 \\ y=(4)/(5)x-8+9 \\ y=(4)/(5)x+1 \end{gathered}`

Therefore, Vladimir is right.

Robyn says that the line also passes throught the points (-10,-7) and (-15,-11). To find out if she is right we need to plu the values of x and y of the points in the equation; if the equation holds then Robyn is also right.

With the point (-10,-7) the equation takes the form:

`\begin{gathered} -7=(4)/(5)(-10)+1 \\ -7=-(40)/(5)+1 \\ -7=-8+7 \\ -7=-7 \end{gathered}`

then, the line passes through the point (-10,-7).

With the point (-15,-11) the equation takes the form:

`\begin{gathered} -11=(4)/(5)(-15)+1 \\ -11=-(60)/(5)+1 \\ -11=-12+1 \\ -11=-11 \end{gathered}`

then, the line passes through the point (-15,-11).

Therefore, Robyn is correct.

In conclusion, they are both correct.