Question 641779
The slope of a line is the tangent of the smaller angle it makes with the positive x-axis.
{{{drawing(300,300,0.7,1.7,-0.2,0.8,
grid(0),
blue(line(0.7,-0.1,1.7,0.9)),
green(triangle(0.8,-0.01,1.3,0.49,1.3,-0.01)),
locate(0.85,0.05,angle),
locate(0.99,-0.002,DELTAx),locate(1.31,0.3,DELTAy)
)}}} In the green right triangle, {{{tan(angle)=DELTAy/DELTAx=slope}}}
In this case, {{{tan(45^o)=1}}} is the slope of the line
The point-slope form of the line we want, using point (3,5) is
{{{y-5=1*(x-3)}}}
That simplifies to {{{y-5=x-3}}} ,
and adding 5 to both sides of the equal sign,
we get the equivalent, more popular,and unique slope-intercept form:
{{{highlight(y=x+2)}}}
{{{drawing(300,300,-3,7,-2,8,
grid(1),
blue(circle(3,5,0.2)),
blue(line(-3,-1,7,9))
)}}}