In slope-intercept form, what is the equation of the line passing through the points (2,13)and (5,22)

y = 3x + 7

Step-by-step explanation:

As we move from (2, 13) to (5, 22), x (the "run") increases by 3 and y (the "rise") increases by 9.  Thus, the slope, m, must be m = rise / run = 9/3, or 3.

Then we have y = 3x + b and must find b.  Subbing 2 for x and 13 for y, we get

13 = 3(2) + b, so that b must be 7.

The desired equation is y = 3x + 7.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this