write an equation of the line that passes through the given point and has the given slope. (1, -5); slope…

Explanation:

Step1: Use the point - slope form

The point - slope form of a line is (y - y_1=m(x - x_1)), where ((x_1,y_1)=(1,-5)) and (m =-\frac{3}{2}). Substitute the values: (y-(-5)=-\frac{3}{2}(x - 1))

Step2: Simplify the equation

(y + 5=-\frac{3}{2}x+\frac{3}{2}) Subtract 5 from both sides: (y=-\frac{3}{2}x+\frac{3}{2}-5) (y=-\frac{3}{2}x+\frac{3 - 10}{2}) (y=-\frac{3}{2}x-\frac{7}{2})

Answer:

(y =-\frac{3}{2}x-\frac{7}{2})