Question

From the choices given below choose the equation whose graphs are given in Fig. 4.7

1) y=x+2
2) y=x-2
3) y=-x+2
4) x+2y=6​

Answer 1

Answer:

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Step-by-step explanation:

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$Method \: I = \\ so \: here \: for \: certain \: line \\ let \: \: ( - 1,3) = (x1,y1) \\ (2,0) = (x2,y2) \\ \\ so \: slope \: of \: this \: line \: (m)= \frac{y2 - y1}{x2 - x1} \\ \\ = \frac{0 - 3}{2 - ( - 1)} \\ \\ = \frac{ - 3}{2 + 1} \\ \\ = \frac{ - 3}{3} \\ \\ = - 1 \\ ie \: \: m = - 1 \\ \\ so \: we \: know \: that \\ equation \: of \: slope \: point \: form \: is \: given \: by \\ (y - y1) = m.(x - x1) \\ (y - 3) = - 1(x - ( - 1)) \\ y - 3 = - 1(x + 1) \\ y - 3 = - x - 1 \\ y = - x - 1 + 3 \\ \\ ie \: \: y = - x + 2$

$Method \: II = \\ so \: here \: x - intercept \: a \: is \: 2 \: and \: also \: y \: intercept \: b \: is \: 2 \\ so \: let \: (a,b) = (2,2) \\ so \: we \: know \: \: that \: equation \: of \: double \: intercept \: form \: \: is \: given \: by \\ \frac{x}{a} + \frac{y}{b} = 1 \\ \\ \frac{x}{2} + \frac{y}{2} = 1 \\ \\ \frac{2x + 2y}{4} = 1 \\ \\ 2x + 2y = 4 \\ dividing \: throughout \: by \: 2 \\ we \: get \\ x + y = 2 \\ ie \: \: y = 2 - x \\ hence \: \: y = - x + 2$

$Method \: III \\ use \: slope \: intercept \: form \: equation \: ie \\ y = mx + c \: \: wherein \: c \: \: is \: \: intercept$

$Method \: IV = \\ use \: two \: points \: form \: equation \: ie \\ \frac{x - x1}{x1 - x2} = \frac{y - y1}{y1 - y2}$