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#### The points Q (1, 3) and R (7, 0) lie on the line l_1, as shown in the diagram above.

286 viewed last edited 5 years ago Anonymous
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The line l_2 is perpendicular to   l_1 passes through Q and crosses the y-axis at the point P, as shown in the diagram above.

i) Find an equation for   l_2,

ii) Find the coordinates of P,  Krishna
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i) Find an equation for  l_2

Step 1: Calculate the slope of the given line equation

NOTE: Putting the equation in the form y = mx (+c) and attempting to

extract the m

Step 2: Find the slope of the another line

NOTE: i) Parallel lines have the same slope.

ii) Perpendicular lines have slopes that are opposite reciprocals, like

\frac{a}{b} \text{ and } \frac{-b}{a}. The slopes also have a product of -1

Step 3: Use the slope of line and a point on line to find its y - intercept.

EXAMPLE: Plug the slope m = -2 and the point (-6, 4) into the

slope-  intercept formula. Then solve for the y-intercept b.

y = mx + b

4 = -2(-6) + b

Step 4: Use the slope of line and the y-intercept of line to find the equation of the line.

EXAMPLE: Plug the slope m = -2 and the y-intercept b = -8 into the

slope- intercept formula.

y = mx + b

y = -2x + -8

ii) Find the coordinates of P,

Step 1: Calculate the point by the given hints in the question

NOTE: The point lies on the y-axis so the x-coordinate is zero

point p = (0, y)

Step 1: Substitute this point on the line equation and simplify you will get the unknown variable.

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