So solve for the equations of the lines y=mx+b m=slope b=y intercept
line 1= (-4,5) (0,2) (x,y) slope=(y1-y2)/(x1-x2) x1=-4 y1=5 x2=0 y2=2 subsitute (5-2)/(-4-0)=3/-4=-3/4 slope=-3/4 subsitute y=-3/4x+b subsitute one of the points (0,2) x=0 and y=2 is one solution 2=-3/4(0)+b 2=0+b 2=b the equation is y=-3/4x+2
other line (0,5) (4,2) x1=0 y1=5 x2=4 y2=2 sybsitute (5-2)/(0-4)=3/-4=-3/4 slope=-3/4 subsitute y=-3/4x+b now subsitute one of the points to solve for b (0,5) x=0 and y=5 is one solution 5=-3/4(0)+b 5=0+b 5=b y=-3/4x+5
so we have the lines/equations y=-3/4x+2 and y=-3/4x+5 (at this point we can see that since slopes are the same and the y intercepts are different, they are paralell and therefor have 0 solutions, but for those who don't know paralellline thingie read on)
solve for common (x,y) y=-3/4x+2 y=-3/4x+5 subsitute -3/4x+2=y=-3/4x+5 -3/4x+2=-3/4x+5 subtract 2 from both sides -3/4x=-3/4x+5 add 3/4x to both sides 0=5 fasle there are no solutions
