wirte an equation in slope- intercept form of the line that passes through the given point and is parallel to the graph of the given points
(2,-1) y = (3/2)x +6
Slope intercept form is y = mx + b where m = gradient and b = y intercept.
equation (1) is y = -4x - 1 is already in this form, m=-4 and b = -1
perpendicular lines m1 x m2 = -1 (i.e. each slope is negative inverse of the other)
-4 x m2 = -1 => m2 = 1/4
equation of perpendicular line is y = 1/4 x + c
substitute point values (1, -3) to find c:
-3 = 1/4 (1) + c => -3 - 1/4 = c => c = -13/4
hence required equation is y = 1/4 x - 13/4 which is equivalent to 4y = x - 13
now do the same with equation (2) y = x + 3 where m = 1 and b = ?
m1 x m2 = -1
1 x m2 = -1 => m2 = ?
required equation of perpendicular line is therefore y =
you have figure out what y equals
since the new line is parallel to y = (3/2)x + 6, it will differ only in the constant
so let new line be
y = (3/2)x + b, but (2,-1) lies on it, so
-1 = (3/2)(2) + b
-1 = 3 + b
b = -4
y = (3/2)x - 4
i did to much
To find an equation in slope-intercept form (y = mx + b) for a line that is parallel to the given line (y = (3/2)x + 6) and passes through the point (2, -1), we need to follow these steps:
Step 1: Understand the slope-intercept form
The slope-intercept form of a linear equation is given as y = mx + b, where:
- "m" represents the slope of the line
- "b" represents the y-intercept (the point where the line intersects the y-axis)
Step 2: Find the slope of the given line
In the given line equation (y = (3/2)x + 6), the coefficient of "x" (3/2) represents the slope of the line. Therefore, the slope of the given line is 3/2.
Step 3: Determine the slope of the parallel line
Since the parallel line has the same slope as the given line, the slope of the parallel line is also 3/2.
Step 4: Substitute the slope and the given point into the equation
Using the slope-intercept form (y = mx + b), we can substitute the slope (3/2) and the given point (2, -1) into the equation. So we have:
- Substitute m = 3/2
- Substitute x = 2
- Substitute y = -1
The equation becomes:
-1 = (3/2)(2) + b
Step 5: Solve for the y-intercept (b)
To solve for the y-intercept (b), we can simplify the equation and isolate the variable b:
-1 = 3 + b
Subtract 3 from both sides:
-1 - 3 = b
-4 = b
So the y-intercept (b) is -4.
Step 6: Write the final equation
Now that we have the slope (3/2) and the y-intercept (-4), we can write the final equation in slope-intercept form (y = mx + b):
y = (3/2)x - 4
Therefore, the equation in slope-intercept form for the line that is parallel to the given line (y = (3/2)x + 6) and passes through the point (2, -1) is y = (3/2)x - 4.