Write an equation in point-slope form for the line through the given point with the given slope.

Question

(4, –6); m = 3/5

Answer 1

To write an equation in point-slope form, we use the formula:

\[ y - y_1 = m(x - x_1) \]

where \( (x_1, y_1) \) is the given point and \( m \) is the slope.

Given the point \( (4, -6) \) and the slope \( m = \frac{3}{5} \), we can plug these values into the formula:

\[ y - (-6) = \frac{3}{5}(x - 4) \]

Simplifying this gives:

\[ y + 6 = \frac{3}{5}(x - 4) \]

So the equation in point-slope form is:

\[ y + 6 = \frac{3}{5}(x - 4) \]