The equation of the line in point-slope form is <u>y - 6 = (-1/2)(x - (-3))</u> which can be simplified as <u>x + 2y = 9</u>.
The equation of a line that has a slope m, and passes through the point (x₁, y₁) is given by the point-slope form of a line, which can be shown as:
(y - y₁) = m(x - x₁).
In the question, we are asked to find the equation of the line in point-slope form, that passes through the point (-3, 6) and has a slope m = -1/2.
We know that the equation of a line that has a slope m, and passes through the point (x₁, y₁) is given by the point-slope form of a line, which can be shown as:
(y - y₁) = m(x - x₁).
Taking (x₁, y₁) as (-3, 6) and m = -1/2, in the point-slope form, we get the equation of the line as;
y - 6 = (-1/2)(x - (-3)).
This can be simplified as:
2y - 12 = - x - 3,
or, x + 2y = 9.
Thus, the equation of the line in point-slope form is <u>y - 6 = (-1/2)(x - (-3))</u> which can be simplified as <u>x + 2y = 9</u>.
Learn more about the point-slope form at
brainly.com/question/11624671
#SPJ9
