which point - slope equation represents a line that passes through (3, - 2) with a slope of…

which point - slope equation represents a line that passes through (3, - 2) with a slope of - \\frac{4}{5}?\n\\( y - 3 = - \\frac{4}{5}(x + 2) \\)\n\\( y - 2 = \\frac{4}{5}(x - 3) \\)\n\\( y + 2 = - \\frac{4}{5}(x - 3) \\)\n\\( y + 3 = \\frac{4}{5}(x + 2) \\)

which point - slope equation represents a line that passes through (3, - 2) with a slope of - \\frac{4}{5}?\n\\( y - 3 = - \\frac{4}{5}(x + 2) \\)\n\\( y - 2 = \\frac{4}{5}(x - 3) \\)\n\\( y + 2 = - \\frac{4}{5}(x - 3) \\)\n\\( y + 3 = \\frac{4}{5}(x + 2) \\)

Answer

Explanation:

Step1: Recall the point - slope formula

The point - slope formula is (y - y_1=m(x - x_1)), where ((x_1,y_1)) is a point on the line and (m) is the slope.

Step2: Identify the values of (x_1,y_1) and (m)

Given the point ((3,-2)), so (x_1 = 3) and (y_1=-2). The slope (m =-\frac{4}{5}).

Step3: Substitute the values into the formula

Substitute (x_1 = 3), (y_1=-2) and (m =-\frac{4}{5}) into (y - y_1=m(x - x_1)). We get (y-(-2)=-\frac{4}{5}(x - 3)), which simplifies to (y + 2=-\frac{4}{5}(x - 3)).

Answer:

(y + 2=-\frac{4}{5}(x - 3)) (the third option)