Find the equation of the line, in slope-intercept form, that satisfies the given conditions.

The graph is perpendicular to the graph of y = 5x − 9 and passes through the point whose coordinates are (3, −1).

slope = -1/5

y = -(1/5)x + b

-1 = -3/5 + b
b = -2/5
so
y = -(1/5)x -2/5
or
5 y = -x -2

To find the equation of a line that is perpendicular to the given line y = 5x - 9, we can use the fact that the slopes of perpendicular lines are negative reciprocals.

The given line has a slope of 5 (since it is in the form y = mx + b, where m is the slope). The slope of the line perpendicular to it will be -1/5.

Now, we can use the point-slope form of a line to find the equation. The point-slope form is:

y - y1 = m(x - x1)

where (x1, y1) are the coordinates of the given point and m is the slope.

Plugging in the values, we have:

y - (-1) = (-1/5)(x - 3)

Simplifying, we get:

y + 1 = (-1/5)x + 3/5

To convert the equation to slope-intercept form (y = mx + b), we can isolate y:

y = (-1/5)x + 3/5 - 1

Simplifying further, we have:

y = (-1/5)x + 3/5 - 5/5

y = (-1/5)x - 2/5

Therefore, the equation of the line, in slope-intercept form, that satisfies the given conditions is y = (-1/5)x - 2/5.

To find the equation of the line that is perpendicular to the given line and passes through the given point, we need to follow these steps:

Step 1: Determine the slope of the given line.
The given line equation is y = 5x - 9, which is in slope-intercept form (y = mx + b), where m represents the slope. The slope of the line is 5.

Step 2: Determine the slope of the line perpendicular to the given line.
Since the line we want to find is perpendicular to the given line, the slope of the perpendicular line will be the negative reciprocal of the slope of the given line. To find the negative reciprocal, we take the reciprocal of 5 (1/5) and change the sign to negative (-1/5). Therefore, the slope of the perpendicular line is -1/5.

Step 3: Use the point-slope form to find the equation.
The point-slope form of a line is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. We have a point (3, -1) and the slope -1/5, substituting these values into the equation, we get:
y - (-1) = -1/5(x - 3)
y + 1 = -1/5(x - 3)

Step 4: Simplify the equation to slope-intercept form.
To convert the equation to slope-intercept form (y = mx + b), we need to simplify it further:
y + 1 = -1/5(x - 3)
y + 1 = -1/5x + 3/5
Subtracting 1 from both sides:
y = -1/5x + 3/5 - 1
y = -1/5x + 3/5 - 5/5
y = -1/5x - 2/5

So, the equation of the line that is perpendicular to y = 5x - 9 and passes through the point (3, -1) is y = -1/5x - 2/5 in slope-intercept form.