a line has a slope of $-\\frac{3}{4}$ and passes through the point $(5, -4)$. write its equation in slope…

a line has a slope of $-\\frac{3}{4}$ and passes through the point $(5, -4)$. write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

a line has a slope of $-\\frac{3}{4}$ and passes through the point $(5, -4)$. write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer

Explanation:

Step1: Use the point - slope form

The point - slope form of a line is (y - y_1=m(x - x_1)), where (m =-\frac{3}{4}), (x_1 = 5), and (y_1=-4). Substitute these values into the formula: (y-(-4)=-\frac{3}{4}(x - 5)). Simplify to get (y + 4=-\frac{3}{4}(x - 5)).

Step2: Distribute the slope

Distribute (-\frac{3}{4}) on the right - hand side: (y+4=-\frac{3}{4}x+\frac{15}{4}).

Step3: Solve for (y)

Subtract 4 from both sides. Since (4=\frac{16}{4}), we have (y=-\frac{3}{4}x+\frac{15}{4}-\frac{16}{4}). Simplify the right - hand side: (y=-\frac{3}{4}x-\frac{1}{4}).

Answer:

(y =-\frac{3}{4}x-\frac{1}{4})