coordinate geometry – straight lines - The line l_1 has equation 3x + 5y – 2 = 0. The line l_2 is perpendicular to l_1 and passes through the point (3, 1).

Krishna (last edited 5 years ago) (Expert, Educator @Qalaxia)

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