Question

# Find the x-and y-intercepts of the graph of the equation algebraically. y=5-(6-x)

Upper level algebra
Find the x-and y-intercepts of the graph of the equation algebraically.
$$\displaystyle{y}={5}-{\left({6}-{x}\right)}$$

2021-02-10
Calculation:
Consider, the equation, $$\displaystyle{y}={5}-{\left({6}—{x}\right)}$$,
To compute x-intercept, put $$\displaystyle{y}={0}$$.
$$\displaystyle{0}={5}-{\left({6}-{x}\right)}$$
Opening the bracket, multiply by -1, this gives,
$$\displaystyle{0}={5}-{6}+{x}$$
$$\displaystyle{0}=-{1}+{x}$$
$$\displaystyle{x}={1}$$
So, the x-intercept is (1,0).
To compute y-intercept, put $$\displaystyle{x}={0}$$.
$$\displaystyle{y}={5}-{\left({6}-{0}\right)}$$
$$\displaystyle{y}={5}-{6}$$
$$\displaystyle{y}=-{1}$$
So, the y -intercept is (0, -1).
Hence, the x and y -intercepts of $$\displaystyle{y}={5}-{\left({6}-{x}\right)}$$ are (1,0) and (0,-1),respectively.