Answer: x and y intercepts are the points in which your line crossing x axcis and y axcis . For the streight line given by linear function y=ax+b we find coordinates of the point A represent x intercept using value for the second coordinate y=0 then return this value to linear function
0=ax+b subtract b from both sides
-b -b
-b=ax divide by a which id different then 0
-b/a=x
X-itercept is a point A(-b/a, 0)
For y intercept point B (x.y) our first coordinate x=0, return this value to the linear function y=ax+b
y=a*0+b
Y=0+b
y=b
y intercept is a point B(0,b)
For the special types of linear equations:
1. When a=0 liner function is y=b we have parallel lines with x axcise, crosing only y axcise and there are only y intercept B(0,b)
2. When a=0 and b=0 linear function is y=0, which is equation of the x axcise. In this case y intercept is the orgin point O(0,0) and x-intercepts is are all points of the x axcise A(x,0); x can be any real number. This means infinite many x intercept points.
3. When a is not 0 and b=0 we have x intercept point A(0,0) and y intercept point B(0,0).
4. For the linear equation x=c, c is constant value, we have parallel line with y axcise crosing x axcise at the point A(c,0) and there is no y intersect because there are parallel lines
Step-by-step explanation: Example y=2x+6. For x intercept y=0, return to linear function and in the place oy poot its value
0=2x+6 subtract 6
-6 -6
-6=2x divide by 2
-3=x
X intercept points is a point A(-3,0)
For the y intercept point B(x,y) x=0, return to linear function and in the place of x poot its value
y=2x+6
y=2*0+6
y=0+6
y=6
x intercept is a point B(0,6).