What is the equation of the line perpendicular to #y = 3x -2# and passes through point (3,4)?
2 Answers
Explanation:
#"given a line with slope m then the slope of a line "#
#"perpendicular to it is"#
#•color(white)(x)m_(color(red)"perpendicular")=-1/m#
#y=3x-2" is in "color(blue)"slope-intercept form"#
#•color(white)(x)y=mx+b#
#"where m is the slope and b the y-intercept"#
#y=3x-2rArrm=3#
#rArrm_(color(red)"perpendicular")=-1/3#
#rArry=-1/3x+blarr" is the partial equation"#
#"to find b substitute "(3,4)" into the partial equation"#
#4=-1+brArrb=5#
#rArry=-1/3x+5larrcolor(red)" in slope-intercept form"#
Explanation:
Let us take the equation of the line as:
Since the 2 lines are perpendicular, we use the negative reciprocal rule where:
- The product of the lines' slopes should be equal to -1.
From this rule, we get that:
We divide both sides by 3 to get the slope
Equation of line:
To find the y-intercept
Let us call the given point A:
Since A lies on the line:
Adding 1 to both sides to isolate y-intercept b:
Putting the values of