find k so that the line through (3,k) and (1,-2) is parallel to 5x-3y=2. Find k so that the line is perpendicular to 3x+2y=6
I am glad you fixed up this question, since the way you had it a while back made no sense.
The new equation must differ only in the constant, since the slope is the same.
so the new equation must be
5x - 3y = c, but (1,-2) is supposed to be on it, so
5 + 6 = c = 11
new equation: 5x - 3y = 11
if (3,k) is on it also, ...
15 - 3k = 11
-3k = -4
k = 4/3
I am trying so hard I take what is given to me and try to study them. I have a problem with word problems and cannot figure out what I am doing wrong. I did my first two by myself just the other day and was so excited.I learned those problems from this site and got to utilize what was done for me so thanks
To find the value of k so that the line passing through (3, k) and (1, -2) is parallel to the line 5x - 3y = 2:
Step 1: Determine the slope of the given line.
To find the slope of the line 5x - 3y = 2, rearrange the equation in the slope-intercept form (y = mx + b), where m represents the slope:
5x - 3y = 2
-3y = -5x + 2
y = (5/3)x - (2/3)
The slope of the given line is 5/3.
Step 2: Use the slope of the given line to find the slope of the line passing through (3, k) and (1, -2).
The slope formula for two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
Using (3, k) and (1, -2), we can substitute the coordinates into the formula to get:
(5/3) = (k - (-2)) / (3 - 1)
(5/3) = (k + 2) / 2
Cross-multiplying gives:
3(k + 2) = 2(5)
3k + 6 = 10
3k = 4
k = 4/3
So, k = 4/3 if the line passing through (3, k) and (1, -2) is parallel to the line 5x - 3y = 2.
To find the value of k so that the line passing through (3, k) and (1, -2) is perpendicular to the line 3x + 2y = 6:
Step 1: Determine the slope of the given line.
To find the slope of the line 3x + 2y = 6, rearrange the equation in slope-intercept form:
2y = -3x + 6
y = (-3/2)x + 3
The slope of the given line is -3/2.
Step 2: Use the negative reciprocal of the slope of the given line to find the slope of the line passing through (3, k) and (1, -2).
The slope of a perpendicular line is the negative reciprocal of the slope of the given line. So, the slope of the line passing through (3, k) and (1, -2) is 2/3 (since -3/2 * 2/3 = -1).
Using (3, k) and (1, -2), we can substitute the coordinates into the slope formula to get:
(2/3) = (k - (-2)) / (3 - 1)
(2/3) = (k + 2) / 2
Cross-multiplying gives:
3(k + 2) = 2(2)
3k + 6 = 4
3k = -2
k = -2/3
Therefore, k = -2/3 if the line passing through (3, k) and (1, -2) is perpendicular to the line 3x + 2y = 6.