Write an equation in point-slope form for the line through the given point with the given slope. (-4, 6); m=3/4
A. y-6=3/4x+4
B. y-6=3/4 (x+4)
C. y-6=3/4 (x-4)
D. y-6=3/4 (x+4)
recall that the line through (h,k) with slope m is
y-k = m(x-h)
so, plug in your numbers.
So C?
almost.
(x-(-4)) = x+4, right?
Ya, so D?
B was supposed to be y-6=3/4 (x-4), not +4, so sry for any confusion
(-4, 6), (x, y), m = 3/4.
m = (y-6)/(x-(-4)) = 3/4.
cross multiply:
4(y-6) = 3(x+4),
y-6 = 3/4(x+4).
To write the equation of a line in point-slope form, we need the coordinates of a point on the line and the slope of the line.
Given: Coordinates of a point (-4, 6) and slope m = 3/4
The point-slope form of a linear equation is given by:
y - y₁ = m(x - x₁)
Substituting the given values into the point-slope form, we have:
y - 6 = (3/4)(x - (-4))
Simplifying:
y - 6 = (3/4)(x + 4)
This equation matches option B:
y - 6 = 3/4 (x + 4)
So, the answer is B.