Question

Is the line through the points R(−1, 3) and S(2, −7) parallel to the graph of the line given by the equation, 10x + 3y = 6? (1 point)
No, the slopes have opposite signs.
Yes, the slopes have the same sign and value.
--->Yes, the lines both decrease to the right.
No, the lines have unequal slopes.

Answer 1

10x + 3y = 6
3y = -10x + 6
y = -10/3x + 2 -- slope is -10/3

(-1,3) x1 = -1 and y1 = 3
(2,-7) x2 = 2 and y2 = -7
lets find the slope using the slope formula :
slope(m) = (y2 - y1) / (x2 - x1)
m = (-7 - 3) / (2 -(- 1)
m = -10/3 -- same slope

yes, the slopes have the same sign and value.

Answer 2

Thank you a lot that explanation helped :)

Answer 3

no problem :)

Answer 4

another way to view this is; parallel lines have the same equations, but differ at most by a constant:

10x + 3y = 6 is parallel to 10x + 3y = k

if we insert the values of R and S, and they equate, then they are on the same line that is parallel to the given line.

does: 10(-1) + 3(3) = 10(2) + 3(-7) ??

Answer 5

I didn't think about it that way....thanks amistre, I learn something new everyday :)

Answer 6

Yeah same here thanks