Question

已知直线y=ax+b(b>0)与y轴交于点N,与x轴交于点A且与直线y=kx交于点M（2,3）,

Answer 1

⑴Y=KX过M(2,3),∴3=2K,K=3/2,∴Y=3/2X.

Y=ax+b过M(2,3),则2a+b=3,b=3-2a,

∴Y=aX+(3-2a),

SΔOMN=1/2|3-2a|*2=|3-2a|=5,

∴2a-3=±5,a=4或a=-1,

∴直线Y=aX+b的解析式为Y=4X+5或Y=-X-5,

⑵①当Y=4X+5时,令Y=0得X=-5/4,Y=4X+5与X轴交于A(-5/4,0),

SΔOAM=1/2*5/4*3=15/8,

②当Y=-X-5时,令Y=0得X=-5,Y=-X-5与X轴交于B(-5,0),

SΔOBM=1/2*5*3=15/2.