Write the equation of the line passing through the given point with the given slope.
a) point (3,-2) with slope of m=5/3
Answer: y-(-2)=5/3x-3
b) point (3,9) with slope m=(-2/7)
Answer: y-9=-2/7x-3
Correct?
not quite
y-(-2)=(5/3)(x-3)
3(y+2) = 5(x-3)
3y + 6 = 5x - 15
re-arranging ...
5x - 3y = 21
You have the same error in the second one, watch your brackets.
I see it thanks...
Yes, your answers are correct. The equations of lines can be determined using the point-slope form equation, which is:
y - y1 = m(x - x1)
where (x1, y1) represents the coordinates of the given point, and m represents the slope.
a) For point (3, -2) with a slope of m = 5/3, we substitute the values into the equation:
y - (-2) = (5/3)(x - 3)
y + 2 = (5/3)(x - 3)
b) For point (3, 9) with a slope of m = -2/7, we substitute the values into the equation:
y - 9 = (-2/7)(x - 3)
y - 9 = (-2/7)x + (6/7)
y = (-2/7)x + (6/7) + 9
y = (-2/7)x + (6/7) + (63/7)
y = (-2/7)x + (69/7)
Therefore, your answers are correct.