line j has an equation of ( y = -\frac{9}{7}x + \frac{10}{7} ). line k is parallel to line j and passes…

line j has an equation of ( y = -\frac{9}{7}x + \frac{10}{7} ). line k is parallel to line j and passes through ( (-4, 4) ). what is the equation of line k? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

line j has an equation of ( y = -\frac{9}{7}x + \frac{10}{7} ). line k is parallel to line j and passes through ( (-4, 4) ). what is the equation of line k? 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 k

Since line k is parallel to line ( y = -\frac{9}{7}x+\frac{10}{7} ), their slopes are equal. The slope ( m ) of line k is ( -\frac{9}{7} ).

Step2: Use the point - slope form

The point - slope form is ( y - y_1=m(x - x_1) ), where ( (x_1,y_1)=(-4,4) ) and ( m = -\frac{9}{7} ). Substitute the values: ( y - 4=-\frac{9}{7}(x + 4) ).

Step3: Simplify to slope - intercept form

[ \begin{align*} y-4&=-\frac{9}{7}x-\frac{36}{7}\ y&=-\frac{9}{7}x-\frac{36}{7}+4\ y&=-\frac{9}{7}x-\frac{36}{7}+\frac{28}{7}\ y&=-\frac{9}{7}x-\frac{8}{7} \end{align*} ]

Answer:

( y = -\frac{9}{7}x-\frac{8}{7} )