Question

Find the equation of the line passing through the point (1,3)and making an angle of 45° with x = y + 2

Answer 1

Answer:

your solution is as follows

pls mark it as brainliest

Step-by-step explanation:

$to \: find : \\ equation \: of \: straight \: line \: p \\ \\ so \: let \: here \: two \: straight \: lines \: be \\ p \: and \: q \: respectively \\ \\ so \: line \: p \: makes \: an \: angle \: of \: 45 \\ with \: line \: q \: ie \: with \: x - y = 2 \\ \\ so \: we \: know \: that \\ slope = - \frac{a}{b} \\ \\ thus \: then \: \\ slope \: of \:x - y = 2 \: would \: be \\ m1 = - \frac{1}{ - 1} \\ \\ m1= 1$

$moreover \: we \: know \: that \\ tan \: x = | \frac{m1 - m2}{1 + m1.m2} | \\ \\tan \: x = | \frac{m1 - m2}{1 + m1.m2} | \\ \\ tan \: \frac{\pi}{4} = | \frac{1 - m2}{1 + 1.m2} | \\ \\ 1 = \frac{1 - m2}{1 + m2} \\ \\ 1 - m2 = 1 + m2 \\ \\ 2.m = 0 \\ \\ m = 0$

$so \: equation \: of \: line \: passing \: through \\ (1,3) \: and \: having \: slope \: 0 \\ would \: be \: given \: by \\ y - y1 = m(x - x1) \\ \\ y - 3 = 0(x - 1) \\ \\ y - 3 = 0 \\ \\ y = 3$