Final answer:
The equation of the line in point-slope form that passes through (1, −3) with a slope of −5/3 is given by y + 3 = −5/3x + 5/3.
Step-by-step explanation:
To write the equation of a line in point-slope form, we need a point through which the line passes and the slope of the line. The point-slope form of the equation of a line is given by:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is a point on the line and m is the slope. For the line that passes through the point (1, −3) with a slope of −5/3, we can substitute these values into the point-slope form:
y - (−3) = (−5/3)(x - 1)
Simplifying, we get:
y + 3 = −5/3x + 5/3
This is the equation of the line in point-slope form passing through (1, −3) with a slope of −5/3.