What is the slope of a line that passes through the point (−1, 1) and is parallel to a line that passes through (3, 6) and (1, −2)?

Question

Eva Adamson · Accepted Answer

#m = 4# and its equation is #y = 4x + 5#

Parallel lines have the same slope, so we have to find the slope of the line joining the given points first.

Slope = #(y_2-y_1)/(x_2-x_1) " "("subtract the y's")/"subtract the x's"#

#m = (6-(-2))/(3-1) = 8/2 = 4#

The slope of the line parallel to this line is also 4.

We now know the slope and one point of the new line. It's equation can be found using the formula

#y-y_1 = m(x-x_1)#

#y - 1 = 4(x -(-1)#

#y = 4x +4 +1#

#y = 4x + 5#

Isaiah Anthony · Answer

undefined To find the slope of a line parallel to another line, you use the same slope. First, find the slope of the given line using the formula:

slope = (change in y) / (change in x)

slope = (6 - (-2)) / (3 - 1) 
      = (6 + 2) / (3 - 1) 
      = 8 / 2 
      = 4

Now, since the line we want is parallel to this line, it will have the same slope. So, the slope of the line passing through (-1, 1) and parallel to the given line is also 4.