Find the slope of any line perpendicular to the line through the points (0,5) and (-3,-4)

Write the equation of the line passing through each of the given pairs of points. Write the answer in slope-intercept form, where possible. (-1,3) and (4,-2)

You have asked two separate questions.

In the first problem, get the slope of the line between those points. It is
m = (y2-y1)/(x2-x1)
=(-4 -5)/(-3-0) = -9/-3 = 3
The slope of a line perpendicular to that has to be -1/3, because the product of the two slopes must be -1.

In the second problem, first get the slope
m = (-2 -3)/[4-(-1)] = -1
So y = -x + b
Solve for b by requiring
3 = -(-1) + b
b = 2
y = -x +2

To find the slope of a line perpendicular to another line, you need to determine the slope of the given line first.

Step 1: Determine the slope of the line through the points (0,5) and (-3,-4).
Using the formula for slope (m) between two points, which is given by m = (y2 - y1) / (x2 - x1), we can substitute the coordinates into the formula:
m = (-4 - 5) / (-3 - 0) = -9 / -3 = 3.

Step 2: Find the slope of the line perpendicular to the given line.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. In this case, the negative reciprocal of 3 is -1/3.

Therefore, the slope of any line perpendicular to the line passing through the points (0,5) and (-3,-4) is -1/3.

For the second part of your question:

To write the equation of a line passing through two points, (-1,3) and (4,-2), you can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of one of the points.

Step 1: Determine the slope between the two points.
Using the formula for slope (m) between two points:
m = (-2 - 3) / (4 - (-1)) = -5 / 5 = -1.

Step 2: Choose one of the points, for example, (-1,3), and substitute the values of the point and the slope into the point-slope form equation.
y - 3 = -1(x - (-1))
y - 3 = -1(x + 1)

Step 3: Simplify the equation to convert it into slope-intercept form (y = mx + b).
y - 3 = -x - 1
y = -x + 2

Therefore, the equation of the line passing through the points (-1,3) and (4,-2) in slope-intercept form is y = -x + 2.