Question

What is the equation of a line through point (-4,5) that is perpendicular

to the line with equation y= -6x+4?*

Answer 1

The equation of a line through point (-4,5) that is perpendicular to the line with equation y = -6x + 4 is y = 1/6x + 17/3.

Step-by-step explanation:

The equation of a line perpendicular to another can be found by taking the negative reciprocal of the slope of the original line. In this case, the line in question has an equation y = -6x + 4. Since the slope (m) is -6, the perpendicular slope would be 1/6. Now, using the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes and m is the slope, we can find the equation of the line that passes through (-4, 5) and has a slope of 1/6.

The equation becomes y - 5 = 1/6(x + 4). To find the slope-intercept form, distribute and simplify to get y = 1/6x + 5 + 2/3 or y = 1/6x + 17/3.

Answer 2

set two equation of line y=ax+b and y=cx+d

when these two lines are perpendicular to each other, then a*c=(-1)

set answer is y=ax+b

we can know that a=1/6

bring in a=1/6 and(-4,5)

5=(1/6)*(-4)+b

=>5=(-2/3)=b

=>b=5 2/3

answer is y=(1/6)x+5 2/3