Question

Can someone please help With this math question please

Answer 1

We know that one of the point of our line is (5,-1). Since our second point has the same y-intercept as $x-3y=6$, we are going to solve for x in that line to identify the y-intercept:
$x-3y=6$
$-3y=6-x$
$y= \frac{6-x}{-3}$
$y= \frac{1}{3}x-2$
Remember that in a line of the form $y=mx+b$ the intercept is (0,b). From this we can infer that the second point of our line is (0,-2)

Now that we have our two point, we can use the slope formula: $m= \frac{y_{2}-y_{1}}{x_{2}-x_{1} }$ to find the slope of our line:
$m= \frac{-2-(-1)}{0-5}$
$m= \frac{-2+1}{-5}$
$m= \frac{-1}{-5}$
$m= \frac{1}{5}$

We can conclude that the slope of our line is $m= \frac{1}{5}$, so the correct answer is C.