Question

1. a line with a slope of 1/3 passes through the point (3, 6) . which point also lies on this line?

Answer 1

1) Substituting into point-slope form, the equation of the line is y-6=⅓(x-3), which rearranges to:

• y-6 = ⅓x - 1
• y = ⅓x + 5

So, we can now substitute in the coordinates of each of the options to see which point lies on the line.

1. 3 = ⅓(6) + 5 -> 3 = 7, which is false.
2. 6 = ⅓(7) + 5 -> 6 = 22/3, which is false.
3. -3 = ⅓(-3) + 5 -> -3 = 4, which is false.
4. 3 = ⅓(-6) + 5 -> 3 = 3, which is true.

So, the answer is (4) (-6, 3)

2) Substituting into point-slope form, the equation of the line is y - 5 = ¾(x-2), which rearranges to:

• y - 5 = 0.75x - 1.5
• y = 0.75x + 3.5

So, we can now substitute in the coordinates of each of the options to see which point lies on the line.

1. 8 = 0.75(6)+3.5 -> 8 = 8, which is true.
2. 9 = 0.75(5) + 3.5 -> 9 = 7.25, which is false.
3. 1 = 0.75(-1) + 3.5 -> 1 = 2.75, which is false.
4. 2 = 0.75(6) + 3.5 -> 2 = 8, which is false.

So, the answer is (1) (6, 8).