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Find the equation of the line passing through the point (1, 1) and parallel to the line 3x+5y+17=0
- a)3x+5y+8=0
- b)5x+3y+8=0
- c)5x+3y-8=0
- d)3x+5y-8=0
Correct answer is option 'D'. Can you explain this answer?
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Find the equation of the line passing through the point (1, 1) and par...
Solution:
To find the equation of the line passing through point (1, 1) and parallel to the line 3x + 5y + 17 = 0, we need to follow the given steps:
Step 1: Write the given equation in slope-intercept form.
3x + 5y + 17 = 0
5y = -3x - 17
y = (-3/5)x - 17/5
Step 2: Identify the slope of the given line.
The given line is in slope-intercept form y = mx + b
where m is the slope of the line.
Thus, the slope of the given line is (-3/5).
Step 3: Identify 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 (-3/5).
Step 4: Use the point-slope form of the equation to find the equation of the parallel line.
The point-slope form of the equation of a line passing through point (x1, y1) with slope m is given by:
y - y1 = m(x - x1)
Substituting the values of (x1, y1) = (1, 1) and m = (-3/5), we get:
y - 1 = (-3/5)(x - 1)
Simplifying the equation, we get:
5y - 5 = -3x + 3
3x + 5y - 8 = 0
Therefore, the equation of the line passing through the point (1, 1) and parallel to the line 3x + 5y + 17 = 0 is 3x + 5y - 8 = 0 (option D).
To find the equation of the line passing through point (1, 1) and parallel to the line 3x + 5y + 17 = 0, we need to follow the given steps:
Step 1: Write the given equation in slope-intercept form.
3x + 5y + 17 = 0
5y = -3x - 17
y = (-3/5)x - 17/5
Step 2: Identify the slope of the given line.
The given line is in slope-intercept form y = mx + b
where m is the slope of the line.
Thus, the slope of the given line is (-3/5).
Step 3: Identify 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 (-3/5).
Step 4: Use the point-slope form of the equation to find the equation of the parallel line.
The point-slope form of the equation of a line passing through point (x1, y1) with slope m is given by:
y - y1 = m(x - x1)
Substituting the values of (x1, y1) = (1, 1) and m = (-3/5), we get:
y - 1 = (-3/5)(x - 1)
Simplifying the equation, we get:
5y - 5 = -3x + 3
3x + 5y - 8 = 0
Therefore, the equation of the line passing through the point (1, 1) and parallel to the line 3x + 5y + 17 = 0 is 3x + 5y - 8 = 0 (option D).
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Find the equation of the line passing through the point (1, 1) and parallel to the line 3x+5y+17=0a)3x+5y+8=0b)5x+3y+8=0c)5x+3y-8=0d)3x+5y-8=0Correct answer is option 'D'. Can you explain this answer?
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