I suspect that the first expression should be the equation 7x-y=27 which is another way of writing the second equation.
This equation can be written in standard form: y=7x-27 showing the relationship between x and y. Their relationship can be represented by a straight line graph. Every point on the line represents a solution to the equation. So since the line has infinite length, there are an infinite number of solutions.
The intercepts provide an easy way of drawing the line. Put x=0 and we get the y-intercept=-27. So we mark this point on the y-axis. Put y=0 and we get the x-intercept=27/7. So we mark this point on the x-axis. Draw a line through these two points and we get the line.