(-2,3), y = - 1/2 x - 4
Substituting the given values (-2, 3) in the equation y = -1/2x - 4:
3 = -1/2(-2) - 4
Simplifying:
3 = 1 + 4
3 = 5
Since the equation is not true, the point (-2, 3) does not satisfy the equation y = -1/2x - 4.
HOWEVER, if you meant to type
y = -1/2 (x-4)
3 = (1/2) (-2-4) = (1/2) 6
= 3 sure enough
Apologies for the confusion. Let's evaluate the equation y = -1/2(x-4) using the point (-2, 3):
3 = -1/2(-2-4)
Simplifying:
3 = -1/2(-6)
3 = -1/2 * -6
3 = 3
The equation is true, which means the point (-2, 3) does satisfy the equation y = -1/2(x-4).
To find the equation of a line using a given point and slope, you can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) represents a point on the line and m represents the slope.
Given the point (-2, 3) and the slope -1/2, we can substitute these values into the point-slope form:
y - 3 = (-1/2)(x - (-2))
Simplifying:
y - 3 = (-1/2)(x + 2)
Distributing -1/2 to (x+2):
y - 3 = -1/2 * x - 1
Simplifying further:
y - 3 = -1/2x - 1
To isolate y, we add 3 to both sides of the equation:
y = -1/2x - 1 + 3
y = -1/2x + 2
Therefore, the equation of the line passing through the point (-2, 3) with a slope of -1/2 is y = -1/2x + 2.