To find a line that is perpendicular to the line represented by x + 2y = 6, we need to find the negative reciprocal of the coefficient of x and y in the given equation.
The given equation is x + 2y = 6.
To find the slope-intercept form of this equation, we need to solve for y:
2y = -x + 6
y = (-1/2)x + 3
The slope of this line is -1/2.
The negative reciprocal of -1/2 will be 2.
So, the slope of the line perpendicular to the given line is 2.
To find the equation of the line that passes through the point (3, -4) with a slope of 2, we can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is the given point and m is the slope.
Using the point (3, -4) and a slope of 2, the equation becomes:
y - (-4) = 2(x - 3)
y + 4 = 2x - 6
To rewrite this equation in standard form, we move all terms to the left side:
2x - y = 10
Therefore, the equation of the line that is perpendicular to x + 2y = 6 and passes through the point (3, -4) is 2x - y = 10.
what equation represents a line that is perpendicular to the line represented by x+2y=6 and passes through the point (3,−4)?
1 answer
1 answer