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Write the equation of a line parallel to the given line but passing through the given point.
y= x+4; (-7, 1)
What does it mean for one line to be parallel to another?
Two lines are said to be parallel to each other, if they do not meet/intersect on producing. The
slopes of parallel lines is equal.
Working
We first fine the slope of the given line. On comparing with the general form
y = mx + b, we see that slope of given line is m = 1 and y intercept is 4
Two parallel lines have same slope. So the slope of the required line is also 1 and it passes through
(-7, 1). We will use the Point Slope Form to find the equation of line - which has slope 1 and is
passing through the ordered pair (-7, 1)
So we get
y – 1 = 1(x – (-7))
y – 1 = 1(x + 7)
y – 1 = x + 7
y = x + 7 + 1
y = x + 8
Write the equation of a line perpendicular to the given line but passing through the given point.
y= -1/2 x + 1; (4, 2)
What does it mean for one line to be perpendicular to another?
Two lines are said to be perpendicular to each other, if they intersect at right angles. The product of
slopes of perpendicular lines is -1.
Working
We first fine the slope of the given line. On comparing with the general form
y = mx + b, we see that slope of given line is m = -1/2 and y intercept is 1
The product of slopes of two perpendicular lines is -1. So the slope of required line is the negative
reciprocal of the given slope = -1/ -1/2 = 2
We will use the Point Slope Form to find the equation of line - which has slope 2 and is passing
through the ordered pair (4, 2)
So we get
y – 2 = 2 (x – 4)
y – 2 = 2x – 8
y = 2x – 8 + 2
y = 2x - 6
