How do you find equation of a line, L which passes through the point (3, -1) and parallel to the line which passes through the points (0,5) and (-2,-3)?

Question

Julia Adams · Accepted Answer

#y=4x-13# #"the equation of a line in "color(blue)"slope-intercept form"# is. #•color(white)(x)y=mx+c# #"where m is the slope and c the y-intercept"# #"calculate m using the "color(blue)"gradient formula"# #•color(white)(x)m=(y_2-y_1)/(x_2-x_1)# #"let "(x_1,y_1)=(0,5)" and "(x_2,y_2)=(-2,-3)# #m=(-3-5)/(-2-0)=(-8)/(-2)=4# #• " Parallel lines have equal slopes"# #y=4x+clarrcolor(blue)"is the partial equation"# #"to find c substitute "(3,-1)" into the partial equation"# #-1=12+crArrc=-1-12=-13# #y=4x-13larrcolor(red)"equation of parallel line"#

Abigail Allen · Answer

undefined To find the equation of a line $L$ that passes through the point $(3, -1)$ and is parallel to the line passing through the points $(0, 5)$ and $(-2, -3)$, follow these steps:

1. Find the slope of the given line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the given points:
   $m = \frac{-3 - 5}{-2 - 0} = \frac{-8}{-2} = 4$

2. Since the line $L$ is parallel to the given line, it will have the same slope $m = 4$.

3. Use the point-slope form of the equation of a line $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is the given point $(3, -1)$ and $m$ is the slope $4$:
   $y - (-1) = 4(x - 3)$

4. Simplify the equation:
   $y + 1 = 4x - 12$

5. Move the constant term to the right side:
   $y = 4x - 12 - 1$

6. Combine the constants:
   $y = 4x - 13$

Therefore, the equation of the line $L$ that passes through the point $(3, -1)$ and is parallel to the line passing through the points $(0, 5)$ and $(-2, -3)$ is $y = 4x - 13$.