Find an equation of the line passing through the point (−1, 3) and parallel to the line joining the points (−3, 4) and (4, −1).
find the slope between the points (−3, 4) and (4, −1), call it m
then using the other point:
y-3 = m(x+1)
put in your value of m, expand it, and change it to whatever form is needed
To find the equation of a line parallel to another line, we need to determine the slope of the given line. The slope of a line passing through two points can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
Given the points (-3, 4) and (4, -1), let's calculate the slope of the line passing through them:
slope = (-1 - 4) / (4 - (-3))
= (-5) / (4 + 3)
= -5 / 7
Since the line we want to find is parallel to this line, it will have the same slope. Now, we can use the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
Substituting the point (-1, 3) into this equation, we get:
3 = (-5 / 7)(-1) + b
3 = 5 / 7 + b
3 - 5 / 7 = b
(21 - 5) / 7 = b
16 / 7 = b
b = 16 / 7
Therefore, the equation of the line parallel to the line passing through (-3, 4) and (4, -1) and passing through the point (-1, 3) is:
y = (-5 / 7)x + (16 / 7)