Question

find the x and y intercepts -3x+5y=30

Answer 1

What you want is to find out what x is when y = 0, and what y is when x = 0. To do this, simply take turns setting x to 0, solve the equation and then y to 0 and solve it again

Answer 2

x intercept, put y = 0 hence -3x = 30 => x = -10 (-10,0)
y intercept, put x = 0, hence 5y = 30 => y = 6 (0,6)