what line queation would pass through (2,6) and is perpendicular to y=4x+6
A line perpendicular to y=4x+6 has a slope of the additive opposite of the reciprocal of the slope:
- 1/(4)
Now use y - y1 = m(x - x1) to find the equation.
y - 6 = -1/4(x - 2)
y - 6 = -x/4 + 1/2
y = -x/4 + 13/2
x/4?
To find a line that passes through the point (2, 6) and is perpendicular to the line y = 4x + 6, we can determine the slope of the given line and then use that slope to find the perpendicular slope.
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope. The given line, y = 4x + 6, is in slope-intercept form, meaning the slope of this line is 4.
To find the perpendicular slope, we take the negative reciprocal of the given slope. The negative reciprocal of 4 is -1/4.
Now, we have the slope (-1/4) and the point (2, 6), so we can use the point-slope form of a linear equation to write the equation of the line:
y - y1 = m(x - x1)
Plugging in the values, we get:
y - 6 = (-1/4)(x - 2)
Simplifying further:
y - 6 = (-1/4)x + 1/2
To express the equation in the slope-intercept form, we can isolate y:
y = (-1/4)x + 1/2 + 6
y = (-1/4)x + 1/2 + 12/2
y = (-1/4)x + 13/2
Therefore, the equation of the line passing through (2, 6) and perpendicular to y = 4x + 6 is y = (-1/4)x + 13/2.