determine the equation of the line passing through the point (-4, 3) and parallel to the line segment joining A(5, -2) and B(3,4)
slope = (4+2)/(3-5) = 6/-2 = -3
so it must be y = -3x + b
plug in the point (-4,3) to find b
To determine the equation of the line passing through the point (-4, 3) and parallel to the line segment joining A(5, -2) and B(3,4), we can follow these steps:
Step 1: Find the slope of the line segment AB.
The slope of the line segment AB is given by the formula:
m = (y2 - y1) / (x2 - x1)
Considering A(5, -2) and B(3,4), we have:
m = (4 - (-2)) / (3 - 5)
= 6 / (-2)
= -3
Step 2: Use the slope of AB to find the slope of the parallel line.
Since the parallel line will have the same slope as AB, the slope of the parallel line is also -3.
Step 3: Use the point-slope form to determine the equation of the line.
The point-slope form of a linear equation is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
Substituting the given point (-4, 3) and the slope -3 into the point-slope form, we get:
y - 3 = -3(x - (-4))
y - 3 = -3(x + 4)
y - 3 = -3x - 12
y = -3x - 12 + 3
y = -3x - 9
Therefore, the equation of the line passing through the point (-4, 3) and parallel to the line segment AB is y = -3x - 9.
To determine the equation of the line passing through the point (-4, 3) and parallel to the line segment joining A(5, -2) and B(3, 4), we need to find the slope of the line segment AB first.
The slope between two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of A(5, -2) and B(3, 4), we can calculate the slope:
m = (4 - (-2)) / (3 - 5) = 6 / -2 = -3
Now that we have the slope of the line segment AB, we know that any line parallel to it will have the same slope. Therefore, the line passing through (-4, 3) and parallel to AB will also have a slope of -3.
We can now use the point-slope form of the equation of a line to find the final equation:
y - y1 = m(x - x1)
Using the point (-4, 3) and the slope m = -3, we fill in the values:
y - 3 = -3(x - (-4))
Simplifying this equation gives:
y - 3 = -3(x + 4)
Expanding the brackets:
y - 3 = -3x - 12
Further rearranging and simplifying:
y = -3x - 12 + 3
y = -3x - 9
Therefore, the equation of the line passing through (-4, 3) and parallel to the line segment joining A(5, -2) and B(3, 4) is y = -3x - 9.