Write the standard form of the equation of the line that passes through the point (4,1) and is parallel to the line 3x + 2y = 5.
Write the standard form of the equation of the line that passes through the point (4,1)and is parallel to the line 3x + 2y = 5.
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The desired equation can be worked out using the following general formula:
y - y1 = m( x -x1) where m is the slope and (x1,y1) is the one point we know - here (4,1)
To get the slope we rearrange the given line as y = -(3/2) x + 5/2 Once in this form we
see that the slope is -(3/2). Since we want a parallel line the slope m also equals -(3/2)
Putting this together we ge
y - 1 = -(3/2) ( x - 4)
This can be rearranged into the slope intercept form.
y = -(3/2) x + 7
The first step is to determine the slope of the equation we're trying to solve for. Since two parallel lines have the same slope, we need to compute the slope (m) of the equation 3x+2y=5. This can be obtained by converting the equation into slope-intercept form (i.e., y=mx+b, where m is the slope):
So, let's first isolate the y term on the left side, by subtracting 3x from both sides, and then simplifying:
Then, let's divide both sides by 2, to obtain slope-intercept form:
y = (-3/2)x+(5/2) From this, we know that the slope (m) is -3/2
The next step is to determine the equation of the line we're being asked to solve for. If we know the slope (in this case m=-3/2) along with any given point on the line ((x0,y0); in this case (4,1)), the equation of the line can be determined as y-y0=m(x-x0)
So substituting, the equation of the line is y-1=(-3/2)(x-4)
We now need to put this into standard form, with both x and y terms on the left side of the equation:
First, distribute the 3/2 on the right side: y-1=(-3/2)x+(3/2)4 or y-1=(-3/2)x+6
Next, add (3/2)x to both sides, add 1 to both sides, and simplify: (3/2)x+y=7
Finally, we can multiply both sides by 2, to eliminate the fraction (3/2): 3x+2y=14 (This is the equation of the new line in standard form).
Hope this helps.
You will use the equation : Y-Y1=m(x-x1) where m is your slope.
Since the lines are parallel they will have the same slope, so first you must solve for the slope, by making the first equation standardized.
The slope is -(3/2)
Now to get the equation of the line using the points (4,1) use the first equation.