Question

Mark points A (4; −3) and B (−2; 6) on the coordinate plane. Draw AB and find the coordinates of the intersection of the line with the x and y axes.

Answer 1

Answer:

Intersection points with x and y axis are (2,0) and (0,3) respectively.

Step-by-step explanation:

Given the two points A(4, −3) and B(−2, 6).

Please refer to the attached image for the graph of line joining the point A and B.

As per graph, the line AB cuts the x and y axis on the points X and Y respectively whose points are X(2,0) and Y(0,3).

Now, let us find the points of intersection of line AB with x and y axis mathematically.

The equation of the line can be given as:

$y = mx+c$

Where (x,y) are the points that lie on the line.

m is the slope and is defined as:

$m = \dfrac{y_2-y_1}{x_2-x_1}$

c is the y intercept

Let us calculate Slope of line:

Here,

$x_2 = -2\\x_1 = 4\\y_2 = 6\\y_1 = -3$

$m = \dfrac{6-(-3)}{-2-4}\\\Rightarrow m =-\dfrac{9}{6}\\\Rightarrow m =-\dfrac{3}{2}$

So, the equation of line become:

$y=-\dfrac{3}{2}x+c$

Putting (x,y) as (4, −3)

$-3=-\dfrac{3}{2}\times 4+c\\\Rightarrow c = 3$

Rewriting the equation of line:

$y=-\dfrac{3}{2}x+3\\\Rightarrow 3x+2y-6=0$

To find intersection point with x axis, let us put y = 0

$3x+2 \times 0 -6=0\\\Rightarrow x=2$

Intersection point with x axis is X(2,0)

To find intersection point with x axis, let us put x = 0

$3\times 0+2 \times -6=0\\\Rightarrow y=3$

Intersection point with x axis is Y(0,3)