through (3 3) perpendicular to y=-3/8x-5

Answer 1

Let's assume that the question asks us to find the equation of a line that passes through the point (3,3) and is perpendicular to the line y = (- 3/8)*x - 5.

Equation of a Line

Let's start by identifying the pieces that we need to construct the equation of a line. The general formula for a line is given by: y = m*x + b, where m is the slope of the line and b is the y-intercept. So in order to construct the equation of our line, we need to determine its slope and its y-intercept.

For the line given in the problem, the slope is (- 3/8), and the y-intercept is (- 5).

Finding the Slope

In order for two lines to be perpendicular, the angle between them must be 90 degrees. If you imagine two perpendicular lines on a graph, you can see that the two lines kind of look like a '+' that might be rotated in some fashion. In order for two lines to be perpendicular, their slopes must be negative reciprocals of one another. It is difficult to explain why this is true in text. To avoid confusion, I encourage you to ask your teacher or use an educational resource to make sure that you understand the reasoning behind this.

The value of the y-intercept is irrelevant for determining if two lines are perpendicular.

Examples

1) A line of the form y = (3)*x + b is perpendicular to a line of the form y = (- 1/3)*x + b.

2) A line of the form y = (- 5)*x + b is perpendicular to a line of the form y = (1/5)*x + b.

3) A line of the form y = (1/2)*x + b is perpendicular to a line of the form y = (- 2)*x + b.

So the slope of the line we are looking for is the negative reciprocal of (-3/8), which is (8/3).

Finding the y-intercept

Now that we have the slope, we have to determine the value of the y-intercept. To do so, we will use the information that our line must pass through the point (3,3). A line passes through all of the points that satisfy its equation. In other words, we can determine if a line passes through any point by plugging the x and y coordinates into the line's equation and checking if the equation is true.

Examples

1) The line given by: y = 3*x + 2 passes through the point (2,8) but not the point (3,4).

2) The line given by: y = (1/2)*x - 1 passes through the point (2,0) but not the point (0,2).

Since we want our line to pass through the point (3,3), and we know the slope is (8/3), we can simply plug in the slope (m), x, and y, to solve for the y-intercept (b) as follows:

y = (8/3)*x + b => 3 = (8/3)*3 + b => 3 = (8) + b => b = (3 - 8) => b = (- 5)

So we found that our slope is (8/3) and our y-intercept is (- 5). The equation of our line that is perpendicular to the line given in the problem and passes through the point (3,3) is:

y = (8/3)*x - 5.

Hope this helps!