Final answer:
The equation of the line passing through the point (-3, 4) with slope -2/3 is y = (-2/3)x + 2.
Step-by-step explanation:
To find the equation of a line, given a point and the slope, we can use the point-slope form of a line's equation, which is:
y - y₁ = m(x - x₁),
where (x₁, y₁) is a point on the line, and m is the slope.
In this case, we are given the point (-3,4) and the slope m = -2/3. Let's apply these values to the point-slope form:
y - 4 = (-2/3)(x - (-3)),
y - 4 = (-2/3)(x + 3).
Now, let's distribute the slope -2/3 across the x + 3:
y - 4 = (-2/3)x + (-2/3) × 3,
y - 4 = (-2/3)x - 2.
Next, we'll add 4 to both sides of the equation to solve for y:
y = (-2/3)x - 2 + 4,
y = (-2/3)x + 2.
Therefore, the equation of the line with a slope of -2/3 that passes through the point (-3,4) is:
y = (-2/3)x + 2.