Question

The equation of line c is y–5=

Answer 1

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the "c" equation

$y-5=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{3}{5}}(x-7)\qquad \impliedby \begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}$

so line "d" is a line with a slope of 3/5 and passes through (1,-1)

$(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad \qquad \stackrel{slope}{m}\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{\cfrac{3}{5}}(x-\stackrel{x_1}{1})\implies y+1=\cfrac{3}{5}(x-1) \\\\\\ y+1=\cfrac{3}{5}x-\cfrac{3}{5}\implies y=\cfrac{3}{5}x-\cfrac{3}{5}-1\implies y=\cfrac{3}{5}x-\cfrac{8}{5}$

Answer 2

Answer:

y + 1 = (3/5)(x - 1)

Step-by-step explanation:

This is point-slope formula. It is super useful bc you can just fill in a point and the slope to make an equation of a line.

y - y = m(x - x)

Fill in the slope in place of the m.

Fill in the (x, y) given into the SECOND spot y and x .

Your equation had 3/5 in the m spot (that'sslope!) Swipe that and stick it in your equation.

Then they gave you a point (1, -1) that is the (x, y) you need to complete the equation.

The first y stays a y, dont fill in a number there. And the first x stays an x dont fill in a number there either.

Fill in second y, m and second x, and done! Its literally a fill in the blank question!

y + 1 = 3/5 (x - 1)