Question

The equation for line u can be written as y=-(9)/(4)x+1. Line v, which is perpendicular to line u, includes the point (-3,2). What is the equation of line v ?

Answer 1

To find the equation of line v, we can use the point-slope form of a linear equation. By knowing that line v is perpendicular to line u, we can determine its slope as the negative reciprocal of the slope of line u. By using the point-slope form and the given point, we can find the equation of line v.

Step-by-step explanation:

To find the equation of line v, we need to determine its slope. Since line v is perpendicular to line u, the slopes of the two lines are negative reciprocals of each other. To find the slope of line v, we invert the slope of line u and change its sign. So, the slope of line v is 4/9.

We also know that line v includes the point (-3,2). We can use the point-slope form of a linear equation to find the equation of line v. Plug in the values for the slope (4/9) and the coordinates of the point (-3,2) into the equation y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Substituting (-3,2) for (x1, y1) and 4/9 for m, we get y - 2 = 4/9(x + 3). Simplifying the equation gives us the equation of line v as y = 4/9x + 38/9.

Answer 2

The equation of line v, which is perpendicular to line u with the equation y = -(9/4)x + 1 and passes through the point (-3, 2), is y = (4/9)x + 10/3.

Step-by-step explanation:

To find the equation of line v that is perpendicular to line u with the equation y = -(9/4)x + 1, we need to determine the slope of line v. The slope m of line u is -(9/4), which means that the slope of line v will be the negative reciprocal, since perpendicular lines have slopes that are negative reciprocals of each other. Hence, the slope of line v is 4/9. Using the point-slope form y - y1 = m(x - x1), where (x1, y1) is the point (-3, 2) on line v, and plugging in the slope and the point, we get:

y - 2 = (4/9)(x - (-3))

Expanding the equation, we get:

y - 2 = (4/9)(x + 3)

Multiplying both sides by 9 to clear the fraction, and then distributing the 4, we get:

9y - 18 = 4x + 12

Finally, to write the equation in slope-intercept form y = mx + b, we get:

y = (4/9)x + (18 + 12)/9

y = (4/9)x + 30/9

y = (4/9)x + 10/3

So, the equation of line v is y = (4/9)x + 10/3.