M Is The point (5,7) and N is (7,-2). Find the equation of a line parallel to MN which passes through the point (1,-3)
For lines to be parallel, they have to have the same slope.
(7 - (-2))/ 5 -7
9/-2 = m
(1,3)
Use the slope and the point to find the equation. There are many ways to do this. One is called the point slope formula:
y - 3 = (-9/2)(x -1)
simplify and solve for y.
To find the equation of a line parallel to MN that passes through the point (1, -3), we need to determine the slope of line MN and use that slope to find the equation of the parallel line.
Step 1: Find the slope of line MN.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula: slope = (y2 - y1) / (x2 - x1)
Using the coordinates of points M(5, 7) and N(7, -2), the slope of MN is:
slope_MN = (-2 - 7) / (7 - 5)
= -9 / 2
Step 2: Identify the slope of the parallel line
Since the parallel line has the same slope as MN, the slope of the parallel line is also -9 / 2.
Step 3: Use the point-slope form to find the equation of the parallel 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.
Plugging in the values into the point-slope form, we have:
y - (-3) = (-9 / 2)(x - 1)
y + 3 = (-9 / 2)(x - 1)
Step 4: Simplify the equation.
To simplify the equation, we can distribute the (-9 / 2) to the terms inside the parentheses.
y + 3 = -9/2 * x + 9/2
Step 5: Rearrange the equation.
To write the equation in slope-intercept form (y = mx + b), we rearrange the equation:
y = -9/2 * x + 9/2 - 3
Simplifying the right side:
y = -9/2 * x - 3/2
Hence, the equation of the line parallel to MN that passes through the point (1, -3) is y = -9/2 * x - 3/2.
To find the equation of a line parallel to MN, we need to determine the slope of line MN and then use that slope to find the equation of the parallel line passing through the given point.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's find the slope of MN using the given points: M(5, 7) and N(7, -2).
slope = (-2 - 7) / (7 - 5)
= -9 / 2
Since the line we are looking for is parallel to MN, it will have the same slope. Therefore, the slope of the line parallel to MN is also -9/2.
Now that we have the slope and a point (1, -3) that the parallel line passes through, we can use the point-slope form of a linear equation to find the equation of the line.
The point-slope form is given by:
y - y1 = m(x - x1)
where:
m is the slope
(x1, y1) is a point on the line
Plugging in the values, we have:
y - (-3) = -9/2(x - 1)
Simplifying the equation:
y + 3 = -9/2(x - 1)
Now, we can distribute -9/2 to obtain the equation in slope-intercept form (y = mx + b):
y + 3 = -9/2x + 9/2
Rearranging the terms, we get:
y = -9/2x + 9/2 - 3
y = -9/2x + 9/2 - 6/2
y = -9/2x + 3/2
Therefore, the equation of the line parallel to MN that passes through the point (1, -3) is y = -9/2x + 3/2.