The equation of the line is given by [tex]y=x+1[/tex]
it is given that [tex]\Delta ABC[/tex] is a right angled tringle with side BC id perpendicular to side EF of [tex]\Delta DE F[/tex].
What is slope-intercept form of equation of line ?
slope-intercept of the line is [tex]y=mx+c[/tex] where,
m is the slope of line,
and c is the y-intercept
Now, first calculating the slope m of of line passing through points (1,2) and (4,5) :
[tex]\begin{aligned}m&=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\&=\frac{5-2}{4-1}\\&=1\end{aligned}[/tex]
Calculating, y-intercept c by substituting (1,2) in equation [tex]y=mx+c[/tex]
[tex]\begin{aligned}y&=mx+c\\2&=1+c\\c&=1\end{aligned}[/tex]
Therefore, the equation of line passing through point (1,2) and (4,5) in slope-intercept form is given by :
[tex]\begin{aligned}y&=mx+c\\y&=x+1\end{aligned}[/tex]
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