Question

A line passing through the points A(-1,1) and B(2,2). Without using graph , state with reason ,from where the line passes in the quadrant.

Answer 1

Answer:

The equation of line is $y=\frac{1}{3}(x)+\frac{4}{3}$. The line passing through first, second and third quadrant.

Step-by-step explanation:

It is given that the line is passing through the points A(-1,1) and B(2,2).

If a line passing through the two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of line AB is

$y-1=\frac{2-1}{2-(-1)}(x-(-1))$

$y-1=\frac{1}{3}(x+1)$

$y=\frac{1}{3}(x)+\frac{1}{3}+1$

$y=\frac{1}{3}(x)+\frac{4}{3}$

Using slope intercept form we can say that the slope of the line is $\frac{1}{3}$ and y-intercept is $\frac{4}{3}$.

Put y=0, to find the x-intercept.

$0=\frac{1}{3}(x)+\frac{4}{3}$

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

$x=-4$

Since the x-intercept is negative, y-intercept is positive and slope is positive, therefore the line passing through first, second and third quadrant.