we have
2x+3y=12
step 1
Find the intercepts
y-intercept -----> is the value of y when the value of x is equal to zero
so
For x=0
2(0)+3y=12
solve for y
3y=12
y=4
The y-intercept is the point (0,4)
Find the x-intercept
the x-intercept is the value of x when the value of y is equal to zero
so
For y=0
2x+3(0)=12
2x=12
x=6
the x-intercept is the point (6,0)
step 2
Find the slope
we have
2x+3y=12
isolate the variable y
3y=-2x+12
divide by 3 both sides
y=(-2/3)x+4
this is the equation of the line in slope intercept form
the slope is m=-2/3
the slope is negative
step 3
Graph the line
to graph the line plot the intercepts and join then
using a graphing tool
see the attached figure
please wair