Question 188085
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Given points: (3,2) & (9,5)
We first find the Slope via Slope-Intercept Form, {{{m=(y[2]-y[1])/(x[2]-x[1])}}}
Substituting,
{{{m=(5-2)/(9-3)=3/6=1/2}}}


Then thru point (3,2) via Slope-Intercept Form, y=mx+b:
{{{2=(1/2)3+b}}}--->{{{2=3/2+b}}}
{{{b=2-3/2=(4-3)/2=1/2}}} Y-Intercept
Also, thru (9,5): (should be the same)
{{{5=(1/2)9+b}}} --->{{{5=9/2+b}}}
{{{b=5-9/2=(10-9)/2=1/2}}}
The Line Eqn ==> <font color=red>y=(1/2)x+(1/2)</font>, Answer
We see graph,
{{{drawing(400,400,-5,12,-5,8,grid(1),graph(400,400,-5,12,-5,8,(1/2)x+(1/2)),green(circle(3,2,.15)),green(circle(9,5,.15)))}}}
Thank you,
Jojo</font>