line q has an equation of ( y - 2 = -\frac{1}{7}(x + 4) ). line r includes the point ( (-7, 3) ) and is…

line q has an equation of ( y - 2 = -\frac{1}{7}(x + 4) ). line r includes the point ( (-7, 3) ) and is parallel to line q. what is the equation of line r? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

line q has an equation of ( y - 2 = -\frac{1}{7}(x + 4) ). line r includes the point ( (-7, 3) ) and is parallel to line q. what is the equation of line r? 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 point - slope form of a line is ( y - y_1=m(x - x_1) ), where ( m ) is the slope. For line ( q:y - 2=-\frac{1}{7}(x + 4) ), the slope ( m_q=-\frac{1}{7} ). Since line ( r ) is parallel to line ( q ), ( m_r=m_q=-\frac{1}{7} ).

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

Line ( r ) passes through the point ((x_1=-7,y_1 = 3)) and has a slope ( m=-\frac{1}{7} ). Using the point - slope form ( y - y_1=m(x - x_1) ), we substitute the values: ( y-3=-\frac{1}{7}(x + 7) )

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

Expand the right - hand side: ( y-3=-\frac{1}{7}x-1 ) Add 3 to both sides of the equation: ( y=-\frac{1}{7}x-1 + 3 ) ( y=-\frac{1}{7}x+2 )

Answer:

( y =-\frac{1}{7}x + 2 )