Find equation of straight line passing through origin (1 0) and (2 1) then find its X and Y intercept using intercept form?

Question

Answer

Equation of a straight line passing through two points
To find the equation of a straight line passing through two points, we first find the slope of the line using the formula:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
Given the points (1, 0) and (2, 1), the slope of the line is:
$$ m = \frac{1 - 0}{2 - 1} = 1 $$
So, the equation of the line passing through these two points is of the form $ y = mx $.

Equation of the line passing through origin
Since the line passes through the origin (0, 0), the equation of the line becomes:
$$ y = mx $$
Substituting the value of $ m = 1 $, we get:
$$ y = x $$

Intercept form of a straight line
The intercept form of a straight line is given by:
$$ \frac{x}{a} + \frac{y}{b} = 1 $$
Where 'a' is the x-intercept and 'b' is the y-intercept.

Finding x-intercept and y-intercept
For the line $ y = x $, the x-intercept occurs where y = 0 and the y-intercept occurs where x = 0.

X-intercept:
Setting y = 0 in the equation y = x, we get:
$$ 0 = x $$
So, the x-intercept is (0, 0).

Y-intercept:
Setting x = 0 in the equation y = x, we get:
$$ y = 0 $$
So, the y-intercept is (0, 0).
Therefore, the x-intercept and y-intercept of the line passing through the points (1, 0) and (2, 1) is (0, 0) and (0, 0) respectively.

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