the equation for line p can be written as ( y = -\frac{5}{4}x - 6 ). line q includes the point ( (5, -8) )…

the equation for line p can be written as ( y = -\frac{5}{4}x - 6 ). line q includes the point ( (5, -8) ) and is parallel to line p. what is the equation of line q? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

the equation for line p can be written as ( y = -\frac{5}{4}x - 6 ). line q includes the point ( (5, -8) ) and is parallel to line p. what is the equation of line q? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answer

Explanation:

Step1: Determine the slope of line ( q )

Parallel lines have the same slope. The slope of line ( p ) is ( m =-\frac{5}{4}), so the slope of line ( q ) is also ( m =-\frac{5}{4}).

Step2: Use the point - slope form ( y - y_1=m(x - x_1) )

We have ( m =-\frac{5}{4}), ( x_1 = 5), and ( y_1=-8). Substitute these values into the point - slope form: ( y-(-8)=-\frac{5}{4}(x - 5) ) ( y + 8=-\frac{5}{4}(x - 5) )

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

Expand the right side: ( y+8=-\frac{5}{4}x+\frac{25}{4} ) Subtract 8 from both sides. Since ( 8=\frac{32}{4}), we have: ( y=-\frac{5}{4}x+\frac{25}{4}-\frac{32}{4} ) ( y=-\frac{5}{4}x-\frac{7}{4} )

Answer:

( y =-\frac{5}{4}x-\frac{7}{4} )