Write an equation for each line in point-slope form and then convert it to standard form

Write an equation of the line parallel to x+2y=6 through (8,3)

Write an equation of the line perpendicular to x+2y=6 through (8,3)

Graph the three lines on the same coordinate plane

I find it easier to work with the given standard-form equation. The parallel line will have the same x- and y-coefficients and a new constant. That constant can be found by substituting the given x- and y-values into the left-side expression:

x + 2y = 8 + 2·3 = 14

The parallel line is x + 2y = 14.

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The perpendicular line will have the x- and y-coefficients swapped and one of them negated. (In standard form, the x-coefficient is positive, so in this case it is convenient to negate the y-coefficient.) Then the perpendicular line through (8, 3) is ...

2x -y = 2·8 -3 = 13

The perpendicular line is 2x - y = 13.

Write an equation for each line in point-slope form and then convert it to standard form Write an equation of the line parallel to x+2y=6 through (8,3) Write an equation of the line perpendicular to x+2y=6 through (8,3) Graph the three lines on the same coordinate plane

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Write an equation for each line in point-slope form and then convert it to standard form

Write an equation of the line parallel to x+2y=6 through (8,3)

Write an equation of the line perpendicular to x+2y=6 through (8,3)

Graph the three lines on the same coordinate plane