Question

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 ?
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Answer 1

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)