#### The straight line l_2 is perpendicular to l_1 with equation y = \frac{2}{3}x - 2 and passes through Q (5, −3).

Find an equation for l_2 in the form ax + by = c, where a, b and c are integer constants.

Anonymous

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Find an equation for l_2 in the form ax + by = c, where a, b and c are integer constants.

Krishna

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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* = m*x* + 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* = m*x* + b

* y* = -2*x* + -8