The equation of the straight line which makes equal intercepts on the coordinate axes and passes through the poijnt (2, 3), is given ba)x+y=5b)2x+3y=5c)x+y=2d)x+y=3Correct answer is option 'A'. Can you explain this answer?

Question

Answer

To find the equation of the straight line that makes equal intercepts on the coordinate axes and passes through the point (2, 3), we can use the slope-intercept form of a line, which is given by:

y = mx + b

where m is the slope of the line and b is the y-intercept.

Let's first find the slope of the line. Since the line makes equal intercepts on the coordinate axes, the x-intercept and y-intercept will have the same absolute value, but with opposite signs. Let's denote their value as a.

The x-intercept will be (-a, 0) and the y-intercept will be (0, -a). We can use the two points (-a, 0) and (0, -a) to find the slope:

m = (y2 - y1) / (x2 - x1)
= (-a - 0) / (0 - (-a))
= -a / a
= -1

Now that we have the slope, we can substitute it into the slope-intercept form of a line along with the coordinates of the given point (2, 3) to find the equation:

y = mx + b
3 = -1 * 2 + b
3 = -2 + b
b = 5

Therefore, the equation of the straight line that makes equal intercepts on the coordinate axes and passes through the point (2, 3) is:

y = -x + 5

The correct answer is option A: x + y = 5, which is the same as y = -x + 5.

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