A straight line through the point A(3, 4) is such that its intercept between the axes is bisected at A, its equation is
- 3x - 4y + 7 = 0
- 4x + 3y = 24
- 3x + 4y = 25
- x + y = 7
The Correct Option is B
Solution and Explanation
$\therefore \, \, 3 = \frac{a + 0}{2} $
$ \Rightarrow a = 6$
and $4 = \frac{0+ b}{2} $
$ \Rightarrow b = 8 $
Thus, equation of line is
$\frac{x}{6} + \frac{y}{8} = 1$
$\Rightarrow \, 4x + 3y = 24$
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Concepts Used:
x-intercepts and y-intercepts
Intercept:
The point where the line or curve crosses the axis of the graph is called intercept. If a point crosses the x-axis, then it is called the x-intercept. If a point crosses the y-axis, then it is called the y-intercept.
The meaning of intercept of a line is the point at which it intersects either the x-axis or y-axis.
X- intercept
The x-intercept represents where the graph crosses the x-axis. The x-intercept of a line gives the idea about the point which crosses the x-axis.
Y-intercept
The y-intercept represents where the graph crosses the y-axis. The y-intercept is a point at which the line crosses the y-axis.
X and Y Intercept Formula:
The x-intercept of a line is the point at which the line crosses the x axis. ( i.e. where the y value equals 0 )
X - intercept = (x, 0)
The y-intercept of a line is the point at which the line crosses the y axis. ( i.e. where the x value equals 0 )
Y - intercept = (0, y)
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