a) The second line: y = (-1/3) + 4 1/3
b) y = 3x + 1
Step-by-step explanation:
a) Given equation: x + 3y = 5
point (1, 4)
we make y the subject of formula:
x + 3y = 5
3y = -x + 5
y = -x/3 + 5/3
y = -1/3(x) + 5/3
Using the equation of line: y = mx + c
where m= slope, c = intercept
when we compare, m = -1/3
For a line to be parallel to another line, their slope must be equal
We insert the the slope and the point given in order to get the equation of the second line.
point (1, 4) = (x, y), y = mx + c
4 = -1/3(1) + c
4 = -1/3 + c
c = 4 + 1/3 = 4 1/3
The second line: y = (-1/3) + 4 1/3
b) For a line to be perpendicular to another, the slope of one of the line should be the negative reciprocal of the other one
The slope of the 1st line = -1/3
The slope of the other line = negative reciprocal of -1/3
reciprocal of -1/3 = -3/1
negative reciprocal = -(-3/1) = 3/1 = 3
slope = 3
The equation of line: y = mx + c, using the point (1, 4) = (x, y)
4 = 3(1) + c
4 = 3 + c
4-3 = c
c = 1
The equation of line becomes:
y = 3x + 1