The Standard Form for a linear equation in two variables, x and y, is Ax + By = C .
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y - 10 = 2(x - 8)
y - 10 = 2x - 16
-2x + y = -16 + 10
-2x + y = -6 , let's multiply equation by (-1)
2x - y = 6 - standard form of given equation.
coordinate of x-intercept is (x , 0) ----> 2x - 0 = 6 ---> x = 3
                         (3 , 0)
coordinate of y-intercept is (0 , y) ----> 2*0 - y = 6 ----> y= -6
                         (0 , -6)

Standart form

y- 10 = 2(x-8)

y-10+10=2x-16+10

y=2x-6

* an x-intercept is a point on the graph where y is zero

if we take y=0

y=2x-6

2x-6=0

2x-6+6=0+6

2x=6

2x/2=6/2

x=3

*a y-intercept is a point on the graph where x is zero

y=2x-6

y=2*0-6

y=-6