Question

what is perpendicular to y=5x+2 and passes through the point (10,-1)? Is it y=-1/5 +1 or is it y= -1/5x +3?

Answer 1

let y=ax+b (D) be perpendicular to y=5x+2

therefore the product of the slopes will be -1

then a*5=-1 which gives a=-1/5

since the line (10,-1) passes through (D) then substitute i. e. -1=10(-1/5)+b

which gives b=1

so the correct answer is y=-1/5x+1

Answer 2

The correct equation of the line that is perpendicular to y=5x+2 and passes through the point (10,-1) is y=-1/5x + 1.

Step-by-step explanation:

The question asks for the equation of a line that is perpendicular to the line given by y=5x+2 and passes through the point (10,-1). To find the equation of this line, we need to determine its slope and use the point-slope form of a linear equation.

Lines that are perpendicular to each other have slopes that are negative reciprocals. The slope of the given line is 5, so the perpendicular line will have a slope of -1/5. Using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, and the point (10, -1) we can substitute the values to solve for b:

y = mx + b
-1 = (-1/5)(10) + b
-1 = -2 + b
b = 1

Therefore, the equation of the line that is perpendicular to y=5x+2 and passes through the point (10,-1) is y = (-1/5)x + 1, which means the correct answer is y=-1/5x + 1, not y=-1/5x + 3.