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:

$m=\frac{y_2-y_1}{x_2-x_1}$

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

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

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

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

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:

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

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

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

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

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

Therefore, Robyn is correct.

In conclusion, they are both correct.