Question

The equation of line t is y - 7 = 5/4(x - 5). Line u includes the point (10, -8) and is perpendicular to line t. Determine the equation of line u.

Answer 1

The equation of line u is y + 8 = (-4/5)(x - 10).

Step-by-step explanation:

To determine the equation of line u, we need to find its slope and its y-intercept. Since line u is perpendicular to line t, the slope of line u will be the negative reciprocal of the slope of line t. So, the slope of line u is -4/5. We also know that line u includes the point (10, -8). Using the point-slope form of a linear equation, we can substitute the slope and the coordinates of the point into the equation y - y1 = m(x - x1) to find the equation of line u.

Using the point (10, -8) and the slope -4/5, the equation of line u is y + 8 = (-4/5)(x - 10).

Answer 2

To determine the equation of line u, we need to find its slope. Since line u is perpendicular to line t, its slope will be the negative reciprocal of the slope of line t. Therefore, the equation of line u is y = -4/5x - 32/5.

Step-by-step explanation:

To determine the equation of line u, we need to find its slope.

Since line u is perpendicular to line t, its slope will be the negative reciprocal of the slope of line t.

Therefore, the slope of line u is -4/5.

Using the point (10, -8) and the slope -4/5, we can use the point-slope form of a linear equation to find the equation of line u.

Plugging in the values, we get:

y - (-8) = -4/5(x - 10)

y + 8 = -4/5(x - 10)

y + 8 = -4/5x + 8/5

y = -4/5x + 8/5 - 8

y = -4/5x + 8/5 - 40/5

y = -4/5x - 32/5

Therefore, the equation of line u is y = -4/5x - 32/5.