Q.14 Find the equation of the straight line passing through the point (5,7) and inclined at  45 0  to x-axis. If it passes through the point P whose ordinate is -7, what is the abscissa of P?

Dear Student,

The solution to the question is as under:

for the equation of the line we will use slope form, i.e.y=mx+c       where m is the slope of line and c is the y-interceptnow, as slope m=tan θand θ=45°hence, m=tan 45°=1So, the equation of line will be,y=x+c.....(i)Now, since line is passing throught (5,7), hence these coordinates must satisfy the equation of line,putting the values as x=5 and y=7 in equation (i), we get,7=5+cor, c=2Hence, equation of the line is,y=x+2.....(ii)
as the line passes through point P whose ordinate is -7and ordinate is the y coordinate of the point,Hence, putting y=-7 in equation (ii), we get,-7=x+2or, x=-7-2or, x=-9Thus, the abscissa of point P is -9

Hope this information will clear your doubts about the topic.

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