Find the x- and y-intercepts of the line that passes through ( 3, -8) and ( -4, 13).

x-intercept = 1/3, y-intercept = 1

Step-by-step explanation:

y = mx + b (general equation where m=gradient, b=constant)

-8 = 3m + b (from first pair of coordinates)

13 = -4m + b (from second pair of coordinates)

3m + b - (-4m + b) = -8 - 13

7m = -21

m = -3

Using one of the linear equations above:

-8 = 3(-3) + b

-8 = -9 + b

b = 1

Therefore, the linear equation is: y = -3x + 1

To find x-intercept:

Let y = 0

0 = -3x + 1

-1 = -3x

x = 1/3

To find y-intercept:

Let x = 0

y = -3(0) + 1

y = 1

Therefore the x-intercept = 1/3 and y-intercept = 1 for the line that passes through (3, -8) and (-4, 13)

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

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step-by-step explanation: