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:
[tex]y = mx+c[/tex]
Where (x,y) are the points that lie on the line.
m is the slope and is defined as:
[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
c is the y intercept
Let us calculate Slope of line:
Here,
[tex]x_2 = -2\\x_1 = 4\\y_2 = 6\\y_1 = -3[/tex]
[tex]m = \dfrac{6-(-3)}{-2-4}\\\Rightarrow m =-\dfrac{9}{6}\\\Rightarrow m =-\dfrac{3}{2}[/tex]
So, the equation of line become:
[tex]y=-\dfrac{3}{2}x+c[/tex]
Putting (x,y) as (4, −3)
[tex]-3=-\dfrac{3}{2}\times 4+c\\\Rightarrow c = 3[/tex]
Rewriting the equation of line:
[tex]y=-\dfrac{3}{2}x+3\\\Rightarrow 3x+2y-6=0[/tex]
To find intersection point with x axis, let us put y = 0
[tex]3x+2 \times 0 -6=0\\\Rightarrow x=2[/tex]
Intersection point with x axis is X(2,0)
To find intersection point with x axis, let us put x = 0
[tex]3\times 0+2 \times -6=0\\\Rightarrow y=3[/tex]
Intersection point with x axis is Y(0,3)
