Find the eqation of the line perpendicular to y=3x-6 that runs through the point (-1, -3)
1 answer:
The coefficient of x in the equation of the given line, 3, is its slope. The slope of the perpendicular line is the negatve reciprocal of that, -1/3. You now have the slope and a point on the perpendicular line, so you can write its equation using the point-slope form:
y = m(x -x₁) +y₁
where m is the slope and (x₁, y₁) is the point.
An equation for your perpendicular line is
y = (-1/3)(x -(-1)) -3
y = (-1/3)x -10/3
The slope-intercept form of the equation of the perpendicular line is ...
y = (-1/3)x -10/3
y = m(x -x₁) +y₁
where m is the slope and (x₁, y₁) is the point.
An equation for your perpendicular line is
y = (-1/3)(x -(-1)) -3
y = (-1/3)x -10/3
The slope-intercept form of the equation of the perpendicular line is ...
y = (-1/3)x -10/3
You might be interested in
Solve by substitution
Just plug in y=-x-1 into y+x=3
So we get:
Simplify that:
And since that is not true, that means this system of equations has no solutions!
Just plug in y=-x-1 into y+x=3
So we get:
Simplify that:
And since that is not true, that means this system of equations has no solutions!