SOLUTION: 6. Tayler claims that when a linear equation is written in general form, Ax + By + C = 0, the intercept of the corresponding graph is always . /1 a. Show that Tayler’s claim

Algebra ->  Linear-equations -> SOLUTION: 6. Tayler claims that when a linear equation is written in general form, Ax + By + C = 0, the intercept of the corresponding graph is always . /1 a. Show that Tayler’s claim      Log On


   

Question 1018655: 6. Tayler claims that when a linear equation is written in general form, Ax + By + C = 0, the intercept of the corresponding graph is always .
/1 a. Show that Tayler’s claim is true for the equation 3x + 5y + 45 = 0.
Answer:
/1 b. Explain why represents the x-intercept. (Hint: What y-value can be substituted into
Ax + By + C = 0 to determine the x-intercept?)
Answer:
/1 c. Tayler’s claim is not true for horizontal lines. Explain why.
Answer:
/1 d. Suggest a similar rule for the y-intercept. Check the rule using 3x + 5y + 45 = 0.
Answer:
/1 e. Will the rule always work?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
...always what?

Try taking the most generalized form you have, and find the x and y intercepts.
Ax%2BBy%2BC=0

Ax=-By-C
let y=0
Ax=B%2A0-C
x=-C%2FA

By=-Ax-C
y=%28-Ax%2FB%29-C%2FB
let x=0
y=-C%2FB

The x intercept will be -C%2FA
and
the y intercept will be -C%2FA.

Watch the signs carefully when you apply this.

What if Horizontal Line?
Slope is 0.
y=mx%2Bb
y=b
y-b=0
Ax%2B1%2Ay-b=0 (Do not confuse the differently cased variables)
but the slope being 0 requires that A=0, and finding y-intercept would give -C%2FA=-%28-b%29%2F0 BUT DIVISION BY ZERO IS IMPOSSIBLE, so this method of finding the x-intercept will not give any result; in any case, as long as the horizontal line is any value other than 0, non-intersecting the x-axis is already known.