Standard Form: Ax + By = C
x-intercept = 9: A(9) + B(0) = C ⇒ 9A = C
y-intercept = 3: A(0) + B(3) = C ⇒ 3B = C
Using substitution, 9A = 3B ⇒ 3A = B
Ax + By = C ⇒ Ax + (3A)y = C
Answer: 3x + 9y = 27 → x + 3y = 9
x intercepts and y intercepts will give us 2 points lying on that line. Then using those points, we can evaluate a, b, and c.
The equation of specified line is: [tex]x + 3y = 9[/tex]
Equation of specified line.
The x intercept, since lying on x axis, has its y ordinate 0, thus its coordinate being (9, 0)
The y intercept, since lying on y axis, has its x abscissa 0, thus its coordinate being (0, 3)
Since both point lies on the given line, thus both will satisfy the equation of that line:
[tex]9a + 0b = c\\ 9a = c[/tex]
and
[tex]0a + 3b = c\\ 3b = c[/tex]
Thus, from both equation:
[tex]9a = v = 3b\\ 9a = 3b\\ 3a = b[/tex]
Thus, equation of line is given by:
[tex]ax + by = c\\ ax + 3ay = 9a\\ \\ \text{Dividing by a on both sides}\\ x + 3y = 9[/tex]
Thus, equation of specified line is [tex]x + 3y = 9[/tex]
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