Question

A line is perpendicular to y = -1/5x+1

Answer 1

Answer:

$y = 5\, x + 26$.

Step-by-step explanation:

Start by finding the slope of the line perpendicular to $y = (-1/5)\, x + 1$.

The slope of $y = (-1/5)\, x + 1$ is $(-1/5)$.

In a plane, if two lines are perpendicular to one another, the product of their slopes would be $(-1)$.

Let $m$ denote the slope of the line perpendicular to $y = (-1/5)\, x + 1$. The expression $(-1/5)\, m$ would denote the product of the slopes of these two lines.

Since these two lines are perpendicular to one another, $(-1/5)\, m = -1$. Solve for $m$: $m = 5$.

The $(-5,\, 1)$ is a point on the requested line. (That is, $x_{1} = -5$ and $y_{1} = 1$.) The slope of that line is found to be $m = 5$. The equation of that line in the point-slope form would be:

$y - 1 = 5\, (x - (-5))$.

Rewrite this point-slope form equation into the slope-intercept form:

$y = 5\, x + 26$.