Find the equation of the line containing (7,11) and parallel to y=6.

Find the equation of the line having x-intercept of 5 and y-intercept of -5.

I know that y=mx+b, b=y-mx, and parallel lines have the same slope

A y = 6 line has zero slope. If it goes through (x,y) =(7, 11), the equation must be y = 11.

For your second question, the line goes through (x,y) = (5,0) and (0,-5). The slope is therefore (-5 -0)/(0 -5) = 1
The equation must be of the form
y = x + b
Plug in the coordinates of either point to solve for b.

To find the equation of the line containing (7,11) and parallel to y=6, we need to determine its slope and substitute it into the point-slope form of a line equation.

Step 1: Determine the slope
Since the given line y=6 is in the form y=mx+b, we can see that the slope is m=0 (since there is no x term). Therefore, any line parallel to y=6 will also have a slope of 0.

Step 2: Substitute the slope and point into the point-slope form
Using the point-slope form of a line equation y-y₁=m(x-x₁), we can substitute the given point (7,11) and the slope m=0 into the equation:
y - 11 = 0(x - 7)
Simplifying this equation gives us:
y - 11 = 0
y = 11

Therefore, the equation of the line containing (7,11) and parallel to y=6 is y = 11.

---------------------------

To find the equation of the line with an x-intercept of 5 and a y-intercept of -5, we can use the slope-intercept form of a line equation, which is y = mx + b.

Step 1: Determine the slope
To find the slope, we need to calculate the rise (change in y) over the run (change in x) between the x-intercept and y-intercept. The x-intercept is (5,0), and the y-intercept is (0,-5). Thus, the rise is -5 and the run is 5.

Step 2: Substitute the slope and intercepts into the slope-intercept form
Using the slope-intercept form y = mx + b, we can substitute the slope m = rise/run = -5/5 = -1 and the y-intercept b = -5 into the equation:
y = -1x - 5
Simplifying gives us:
y = -x - 5

Therefore, the equation of the line with an x-intercept of 5 and a y-intercept of -5 is y = -x - 5.