You are being asked to draw a line perpendicular to the graphed line which passes through the point (-6,5)
The slope of a perpendicular line is the opposite reciprocal: meaning you change the sign (from - to + or from + to -) and flip the numerator and denominator (for example if your slope is -2, the perpendicular line’s slope would be 1/2).
First, find the slope of the graphed line. The two points you are given are (-1, 4) and (-2, 7). The formula for slope is m = (y2 - y1) / (x2 - x1) where m is the slope, and (x1, y1) and (x2, y2) are points. Plugging these points into the slope formula you get:
m = (7-4)/ (-2+1) = 3/-1 = -3.
The opposite reciprocal of -3 is 1/3, so the slope of the new line is 1/3.
In slope-intercept form, equations look like this: y = mx + b. M is your slope, and b is your y-intercept. You know the slope of the perpendicular line is 1/3 but still need to find the y intercept. To do this, first plug in your slope to the formula: y = 1/3x + b. Next, plug in (-6,5) to the equation for x and y and then solve for b.
5 = 1/3(-6) + b
5 = -2 + b
7 = b
Now you know what b is, you now have the full equation of the line: y = 1/3x + 7. You can now graph the line, too.
For #2, you are being asked to draw a line parallel to the graphed line which passes through the point (6,5)
The slope of a parallel line is the same as the slope of the original line.
The two points you are given are (-6,0) and (0,9). Plug these into the slope formula:
m = (9-0)/(0+6) = 9/6
The equation of the parallel line so far is y = 9/6x + b
Plug the point (6,5) into the equation to solve for b.
5 = 9/6(6) + b
5 = 9 + b
-4 = b
The equation is y = 9/6x -4. Now you just have to graph it.
I hope this helps :)