Given the problem: Linear equation that passes through the points of (0,5) and (-5,1).
First, whenever you are asked to find a linear equation that passes through two points, remember its going to be slope intercept equation, or y=mx+b. m is the slope, b is the y-intercept.
The y-intercept is where the line crosses the y-axis. The slope can be written as rise/run. Rise and run right is positive, drop and run left is negative.
So in this case, looking at the first point: (0,5), we can see that the y-intercept is 5. Now let's find the slope. We will start at (-5,1) and go to (0,5). Count how many units we rise/drop and how many units we run. Rise 4, run right 5. So the slope is 4/5. Now put all the information into y=mx+b.
Your answer is y=4/5x+5