1.

1. Consider the line passing through the points (1.3) and (4,9).a) What is the slope of the line ?b) What is the equation of the line ?c) Find the coordinates of the point at which the line cuts the x-axis ?​

Answer»

Answer :-

a.) Slope of the line = \dfrac{2}{1} \:\:\text{or}\:\:2

b.) Equation of the line - y = 2x + 1

c.) The coordinates of the POINT at which the line cuts the x-axis is (-0.5, 0)

Solution :-

Let the points be A(1,3) and B(4,9).

Here,

x_1= 1,\:\:\:\:x_2=4\\y_1 = 3,\:\:\:\:y_2=9

a.) Slope of the line = \dfrac{y_2-y_1}{x_2-x_1}

Slope of the line AB = \dfrac{9-3}{4-1} = \dfrac{6}{3}= \dfrac{2}{1} \:\:\text{or}\:\:2

b.) Equation of the line - y - y_1=m(x - x_1)

y = y coordinate of second point  

m = slope  

x = x coordinate of second point

=> y - 3=2(x-1)

=> y - 3 = 2x -2

=> y = 2x - 2 + 3

=> y = 2x + 1

c.) It is given in the question that we have to FIND the coordinates of the point at which the line cuts the x-axis. This INDICATES that y- coordinate of that point is 0 because it cuts x - axis.

=> y = 2x + 1

=> 0 = 2x + 1

=> -1 = 2x

=> \dfrac{-1}{2} =x

=> -0.5 = x

The point is - (-0.5, 0)


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