Question

Write an equation of the line that passes through $\left(7,\ 10\right)$ and is perpendicular to the line $y=-\frac{1}{5}x-9$ .

Answer 1

The equation of the line that passes through (7, 10) and is perpendicular to the line y = -1/5x - 9 is y = 5x - 25.

Step-by-step explanation:

To write an equation of the line that passes through (7, 10) and is perpendicular to the line y = -½x - 9, we need to first determine the slope of the given line.

Since the slope of the given line is -1/5, the slope of the line perpendicular to it will be the negative reciprocal of this value, which is 5 (since m1 * m2 = -1 for perpendicular lines where m1 and m2 are their slopes).

Next, we use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope.

Inserting the point (7, 10) and the slope 5, the equation becomes y - 10 = 5(x - 7).

Simplifying, we get y - 10 = 5x - 35, and adding 10 to both sides results in y = 5x - 25.

So, the equation of the line that passes through (7, 10) and is perpendicular to y = -1/5x - 9 is y = 5x - 25.