Question

Find the slope of line which makes equal positive intercepts on coordinate axes

Answer 1

Answer:

Step-by-step explanation: the intercept form of a line is

x/a +y/b = 1 ...............(1)

where a is x intercept and b is y intercept

A/Q,

a=b

So,(1)=> x/a +y/a =1

=>x+y =a .......(2)

Again in the gradient or slope form,

(2)=>y = - (1)x + a

Where m or slope is (-1).

Answer 2

The slope of the line which makes equal positive intercepts on coordinate axes will be -1.

Given,

A line makes equal positive intercepts on the coordinate axes.

To find,

The slope of this line.

Solution,

Firstly, the equation of a line that makes 'a' intercept on the x-axis and 'b' on the y-axis, is given as,

$\frac{x}{a} +\frac{y}{b} =1$

Here, it is given that the line makes equal positive intercepts on the x- and y- axes. Let both the intercepts be 'a'.

So when both intercepts are equal, the equation will be,

$\frac{x}{a} +\frac{y}{a} =1$

Simplifying the above equation, we get the equation of this line as,

$x+y=a$

$\implies y=-x+a$

This can be written as,

$y=(-1)x+a$

Now, on comparing the above equation with the slope-intercept form of a line,

y = mx + c

(where,

m = slope, and

c = intercept on the y-axis)

We get,

intercept = a, and,

slope = m = -1.

Therefore, the slope of the line which makes equal positive intercepts on coordinate axes will be -1.