Question

What is the equation of a line, in point-slope form, that passes through (5, -3) and has a slope of 23?

1) y - 5 = 2/3(x + 3)
2) y + 3 = 3/3(x - 5)
3) y - 3 = 2/3(x + 5)
4) y + 5 = 2/3(x - 3)

Answer 1

The equation of a line with a slope of 23 that passes through the point (5, -3) is y + 3 = 23(x - 5), which is the correct point-slope form incorporating the given slope and point. None of the provided options match this equation.

Step-by-step explanation:

The question asks for the equation of a line in the point-slope form that passes through a specific point with a given slope. The point-slope form 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. In this case, the line passes through the point (5, -3) and the slope m is 23. The correct point-slope form of the equation is y + 3 = 23(x - 5), because this form shows the slope and the coordinates of the given point correctly. None of the options provided in the question are correct, as they do not reflect both the given slope and point accurately.