Question

HELP ME PLEASE!!!


Write the equation of the line that it is parallel to = − and passes through
, .

Answer 1

parallel lines, have the same exact slope, hmmm what is the slope of y = -2/3 x + 1/3 anyway? well, low and behold, the equation is already in slope-intercept form, therefore

$\bf ~~y=\stackrel{slope}{-\cfrac{2}{3}}x+\cfrac{1}{3}~~$ has a slope of -2/3.

so we're really looking for a line whose slope is -2/3 and runs through 9,4.

$\bf (\stackrel{x_1}{9}~,~\stackrel{y_1}{4})~\hspace{10em}slope = m\implies -\cfrac{2}{3}\\\\\\\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-4=-\cfrac{2}{3}(x-9)\\\\\\y-4=-\cfrac{2}{3}x+6\implies y=-\cfrac{2}{3}x+10$

Answer 2

Hello!

If we want a parallel line, it needs to have the same slope as the other line. If we look at our first equation, the slope of the line is -2/3. This gives us y=-2/3x+b

To finish our equation, we will want to find b. To do so, we can plug the point (9,4) in for (x,y) and solve for b.

4=-2/3(9)+b

4=-6+b

b=10

This gives us our equation below.

y= -2/3x+10

I hope this helps!