Question

write the equation of the line that is parallel to the line y=-5/3x-2 and goes throught the point (-3,1)

Answer 1

Answer:

y = (-5/3)x - 4

Explanation:

The equation of a line with slope m that goes through the point (x1, y1) is:

$y-y_1=m(x-x_1)_{}$

Additionally, two lines are parallel if they have the same slope.

The slope of the line y = (-5/3)x - 2 is (-5/3) because it is the number beside x.

So, the slope of our line is also -5/3.

Therefore, replacing m by -5/3 and (x1, y1) by (-3, 1), we get that the equation of the line is:

$\begin{gathered} y-1=-\frac{5}{3}(x-(-3)) \\ y-1=-\frac{5}{3}(x+3) \end{gathered}$

Finally, solving for y, we get:

$\begin{gathered} y-1=-\frac{5}{3}x-(\frac{5}{3}\cdot3) \\ y-1=-\frac{5}{3}x-5 \\ y=-\frac{5}{3}x-5+1 \\ y=-\frac{5}{3}x-4 \end{gathered}$

So, the answer is:

y = (-5/3)x - 4