To find the equation for the line perpendicular to y = -5/3x + 11 1/3, we need to determine the slope of the perpendicular line.
The given equation is in slope-intercept form (y = mx + b), where m is the slope. The slope of the given line is -5/3, so the slope of the perpendicular line will be the negative reciprocal of this slope (since perpendicular lines have slopes that multiply to -1).
The negative reciprocal of -5/3 is 3/5.
Now we have the slope (m = 3/5) and a point on the line, P(-2, 3). We can use the point-slope form of a linear equation to find the equation of the line:
y - y₁ = m(x - x₁)
Substituting the known values:
y - 3 = (3/5)(x - (-2))
Simplifying:
y - 3 = (3/5)(x + 2)
Distributing the (3/5):
y - 3 = (3/5)x + 6/5
Finally, isolating y:
y = (3/5)x + 6/5 + 3
y = (3/5)x + 6/5 + 15/5
y = (3/5)x + 21/5
So, the equation for the line perpendicular to y = -5/3x + 11 1/3 and containing point P(-2, 3) is y = (3/5)x + 21/5.
What is the equation for the line perpendicular to y= -5/3x+11 1/3 and containing P(-2, 3)?
1 answer