Question

A line contains the points (-4,1) and (4,6). Decide weather or not each of these points are also on the line(there could be more than one answer):
(0,3.5)
(12,11)
(80,50)
(-1,2.875)

Answer 1

Answer:

The given points (-4,1) and (4,6) are used to find the equation of the line the cross through them. First, we have to find the slope:

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\\m=\frac{6-1}{4-(-4)}=\frac{5}{8}$

Now, we use point-slope formula to find the equation:

$y-y_{1}=m(x-x_{1})\\ y-1=\frac{5}{8} (x-(-4))\\y=\frac{5}{8}x+\frac{20}{8}+1\\y=\frac{5}{8}x+\frac{20+8}{8}\\y=\frac{5}{8}x+\frac{28}{8} \\y=\frac{5}{8}x+\frac{7}{2}$

Now, we test each point to see which is on the line:

For (0, 3.5):

$y=\frac{5}{8}x+\frac{7}{2}$

$3.5=\frac{5}{8}(0)+\frac{7}{2}$

$3.5=\frac{7}{2}$

$3.5=3.5$

So, the first point is on the line, because it satisfies the liner equation.

For (12,11):

$11=\frac{5}{8}(12)+\frac{7}{2}$

$11=\frac{60}{8}+\frac{7}{2}$

$11=7.5+3.5$

$11=11$

This point is also on the line.

For (80,50):

$50=\frac{5}{8}(80)+\frac{7}{2}$

$50=50+3.5$

This point is not on the line, because it doesn't satisfy the linear equation.

For (-1, 2.875):

$2.875=\frac{5}{8}(-1)+\frac{7}{2}$

$2.875=\frac{5}{8}(-1)+\frac{7}{2}$

[tex]2.875=2.875/tex]

This also satisfy the equation.

Therefore, only one point is not on the line. All points on the line are:

(-1, 2.875); (12,11) and (0, 3.5).

Answer 2

it could be either o,3.5 or 80,50

• it also could be both, maybe