Graph the linear equation by finding and plotting its intercept. -x+2y=6
1 answer:
Answer:
y-intercept: (0,3)
x-intercept: (-6,0)
Step-by-step explanation:
put equation into y=mx+b
-x+2y=6 (add x to both sides)
2y=6+x (divide both sides by 2)
y=.5x+3
find y-intercept
set x=0
solve for y, y=3
y-intercept (0,3)
find x-intercept
set y=0
solve for x, x=-6
x-intercept (-6,0)
graph and table confirm values
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An equation without exponents and two variables, is typically a straight line. All the points on the line with integer coordinates are solutions of the equation. Since x and y have to be positive as well, there aren't that many solutions.
Let's see where the line crosses the x-axis, it is where y=0:
x/0.5 + 0 = 18, so x=9 at the intercept. y=0 there, so this is a point on the line, but not a solution to the question (y was supposed to be positive).
Possible values for x are thus limited to 1,2,3,4,5,6 and 7. You can try them all (ie., solve the equation with them) and see for which x values the y is also positive and integer.
You will find that x=4, y=2 is the only pair that satisfies these conditions.
Let's see where the line crosses the x-axis, it is where y=0:
x/0.5 + 0 = 18, so x=9 at the intercept. y=0 there, so this is a point on the line, but not a solution to the question (y was supposed to be positive).
Possible values for x are thus limited to 1,2,3,4,5,6 and 7. You can try them all (ie., solve the equation with them) and see for which x values the y is also positive and integer.
You will find that x=4, y=2 is the only pair that satisfies these conditions.