Question

The equation of line t is y=(7)/(4)x+2. Perpendicular to line t is line u, which passes through he point (2,-2). What is the equation of line u ?

Answer 1

The equation of line u, which is perpendicular to line t (y = (7/4)x + 2) and passes through the point (2, -2), is y = (-4/7)x - 6/7.

Step-by-step explanation:

The equation of line t is given by y = (7/4)x + 2. Here, the slope (m) of line t is 7/4. A line perpendicular to line t, such as line u, will have a slope that is the negative reciprocal of 7/4, which is -4/7. Line u passes through the point (2, -2), so we can use the point-slope form to find the equation for line u.

Point-slope form: y - y1 = m(x - x1)

Substituting the point (2, -2) and the slope -4/7 into the point-slope form yields:

y - (-2) = (-4/7)(x - 2)

Let's simplify this equation:

y + 2 = (-4/7)x + (8/7)

Subtracting 2 from both sides:

y = (-4/7)x + (8/7) - 14/7

y = (-4/7)x - 6/7

Therefore, the equation of line u is y = (-4/7)x - 6/7.

Answer 2

The equation of line u is y - (-2) = (-4/7)(x - 2).

Step-by-step explanation:

To find the equation of a line perpendicular to line t, first, we need to determine the slope of line t. The given equation, y = (7/4)x + 2, is in slope-intercept form, y = mx + b, where m is the slope.

Therefore, the slope of line t is 7/4.

Since lines that are perpendicular have slopes that are negative reciprocals of each other, the slope of the perpendicular line, line u, is -4/7.

Using the point-slope form, y - y1 = m(x - x1), and substituting the slope (-4/7) and the given point (2, -2) into the equation, we can find the equation of line u: y - (-2) = (-4/7)(x - 2).