line r has an equation of ( y + 3 = -\frac{1}{5}(x + 2) ). line s includes the point ( (-10, -8) ) and is…

line r has an equation of ( y + 3 = -\frac{1}{5}(x + 2) ). line s includes the point ( (-10, -8) ) and is parallel to line r. what is the equation of line s? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

line r has an equation of ( y + 3 = -\frac{1}{5}(x + 2) ). line s includes the point ( (-10, -8) ) and is parallel to line r. what is the equation of line s? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answer

Explanation:

Step1: Find the slope of line (r)

The equation of line (r) is in point - slope form (y - y_1=m(x - x_1)), where (m) is the slope. For (y+3 =-\frac{1}{5}(x + 2)), the slope (m_r=-\frac{1}{5}). Since line (s) is parallel to line (r), (m_s=m_r=-\frac{1}{5}).

Step2: Use the point - slope form to find the equation of line (s)

The point - slope form is (y - y_1=m(x - x_1)), with (m =-\frac{1}{5}) and ((x_1,y_1)=(-10,-8)). Substitute into the formula: (y-(-8)=-\frac{1}{5}(x-(-10))), which simplifies to (y + 8=-\frac{1}{5}(x + 10)).

Step3: Convert to slope - intercept form (y=mx + b)

Expand the right side: (y+8=-\frac{1}{5}x-2). Subtract 8 from both sides: (y=-\frac{1}{5}x-2 - 8). Simplify: (y=-\frac{1}{5}x-10).

Answer:

(y =-\frac{1}{5}x-10)