Graph the line that passes through (3, 5), perpendicular to a line whose slope is -1/9.

the lines are perpendicular so new line slope = -1/m where m =-1/9
slope of the line = -1/-1/9 = 9
the slope intercept line equation is y = mx + b. b is y-intercept
y = 9x+b
y -intercept value (b) value can be found by replacing the x and y coordinate values in the
equation with the given point (3, 5)
5 = 9 * 3 + b
5 - 27 = b
b = -22
the line equations is y = 9x -22.

Slope - intercept form line equation is y = mx + b, where m is slope and b is y - intercept.

The line passes through the point (3, 5) and perpendecular to a line whose slope is - 1/9.

Because the slopes of perpendicular lines are negative reciprocals, the slope of the line that is passes through the point (3, 5) is 9.

Now the line equation is y = 9x + b.

Find the y - intercept by substituting the given point in the line equation say (x, y) = (3, 5).

5 = 9(3) + b

b = 5 - 27

b = - 22.

The  line equation is y = 9x - 22.

Graph the line y = 9x - 22 :

The line equation is y = 9x - 22.

Compare the equation with slope - intercept form : y = mx + b.

slope = 9 and y - intercept is - 22.

y - intercept is - 22, so the line crosses the y - axis at (0, - 22).

Using slope find the next point.

Slope = rise/run = 9/1

Start at point (0, - 22), move 9 units up and 1 unit right, then plot the point (1, - 13).

Draw the lines through these points.

Graph :