Find the equation of the line passing through (-5, -4) and parallel to the line passing through (-3,2) and (6,8)
To find the equation of the line passing through (-5, -4) and parallel to the line passing through (-3, 2) and (6, 8), we can follow these steps:
1. Find the slope of the given line: To find the slope (m) of the line passing through (-3, 2) and (6, 8), we use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given coordinates, we get:
m = (8 - 2) / (6 - (-3)) = 6 / 9 = 2/3
2. Parallel lines have equal slopes: Since we want the line passing through (-5, -4) to be parallel to the given line, it will have the same slope of 2/3.
3. Using the slope-intercept form: The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since we already have the slope, we need to find the y-intercept.
4. Substitute the slope and point into the equation to solve for b: Using the point (-5, -4), we have:
-4 = (2/3)(-5) + b
-4 = -10/3 + b
To solve for b, we can add 10/3 on both sides:
-4 + 10/3 = b
-12/3 + 10/3 = b
-2/3 = b
5. Plug the values of m and b into the equation: Now that we have the slope (m = 2/3) and the y-intercept (b = -2/3), we can write the equation of the line as:
y = (2/3)x - 2/3
Therefore, the equation of the line passing through (-5, -4) and parallel to the line passing through (-3, 2) and (6, 8) is y = (2/3)x - 2/3.