y=-3x+6 has a y intercept = 6. the linear equation is already written in slope intercept form, where the constant term is the y intercept
the slope intercept form for a linear equation is y=mx + b, where m=the slope and b= the y intercept
in the given problem m=-3 and b=6=the y intercept, where the line crosses the y axis
x intercept = 2. it's the value that makes y =0, it's the point where the line intersects the x axis
y=-3x +6, plug 2 for x into the equation and y will equal zero
0 = -3(2)+6 = -6+6
or
solve the equation for x
y =-3x+6
y-6 = -3x
(y-6)/-3= x
x = (y-6)/-3 = -y/3 + 2, the constant term is the x intercept, when the equation is solved for x
x= -(0)/3+2
x=2
or the points (0,6) and (2,0) are the y intercept and the x intercept
but convention is to just refer to 6 and 2 as the y and x intercept, depending on how the problem is worded
try sketching a rough graph, it helps to see what's going on, plot the two intercepts, connect them with a straight line and that's the graph of the equation. or graph the equation with a graphing calculator, online or hand held, such as TI-83 or 84. It shows you where the line intersects the axes
basic method is, set x=0 then solve for y, that value is the y intercept
and set y=0, then solve for x, that value is the x intercept
y=-3x+6 = -3(0)+6 = 0+6 = 6 = y intercept
y=-3x+6 = 0, x =-6/-3 = 2 = x intercept
another graphical method is take the slope = m=-3 and the y intercept b=6 = the point (0,6)
and move to the right 1, and down by -3, that gets you to the point (0+1,6-3) = (1,3)
now move to the right 1 more, and down another -3. that gets you to the point (1+1,3-3)=(2,0)= the x intercept
