Question

If a line is passing through (1, 1). This point divides the segment between axes in the ratio 3 : 4. Find the equation of this line. Let consider the line 4x + 3y = 7, which cuts x axis at (a, 0) and y axis at (0, b)

Answer 1

\(1=a+\frac{3}{7}(0-a)=\frac{4a}{7},\)

4a = 7, \(a=\frac{7}{4}\)

\(1=0+\frac{3}{7}\times b=\frac{3b}{7},\)

3b = 7, b = \(\frac{7}{3}\)

Points are \((\frac{7}{4},0)\) and \((0,\frac{7}{3}).\)

Slope = \(\frac{\frac{7}{3}}{\frac{7}{4}}=\frac{7}{3}\times\frac{4}{7}=-\frac{4}{3}\)

Equation = \(\frac{y-1}{x-1}=-\frac{4}{3}\)

\(\Rightarrow\) 3y - 3 = -4x + 4

\(\Rightarrow\) 4x - 3y = 7

Equation 4x + 3y = 7