Question

There is a single point which is a solution to the linear equation y-3= ½ ( x + 4 ) that is obvious because the equation is in point-slope form. There are an infinite number of points that are not so obvious. Find the coordinates of the obvious point, and then find two additional points.

Answer 1

in point slope form

if an equation passes through the point
`(x_1,y_1)` and has a slope of m then the equation is

`y-y_1=m(x-x_1)`

we are given

`y-3=(1)/(2)(x+4)` which can be rewritten as

`y-3=(1)/(2)(x-(-4))`
it passes through (-4,3)

a not obvious point
when x=0
y-3=1/2(0+4)
y-3=1/2(4)
y-3=2
y=5
(0,5) isa not obvious opint

another one?
x=2
y-3=1/2(2+4)
y-3=1/2(6)
y-3=3
y=6
(2,6)



obvious point is (-4,3)
2 not obvious points are (0,5) and (2,6)