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Answer:
[tex]y = x + 1[/tex].
Step-by-step explanation:
Start by finding the slope of this line.
If a slanting line goes through [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex], where [tex]x_{0} \ne x_{1}[/tex], the slope of this line would be:
[tex]\begin{aligned}m &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}}\end{aligned}[/tex].
The line in this question goes through [tex](5,\, 6)[/tex] and [tex](3,\, 4)[/tex]. Hence, the slope of this line would be:
[tex]\begin{aligned}m &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}} \\ &= \frac{6 - 4}{5 - 3} \\ &= 1\end{aligned}[/tex].
If a slanting line with a slope of [tex]m[/tex] and goes through the point [tex](x_{0},\, y_{0})[/tex], the equation of this line in the point-slope form would be:
[tex]y - y_{0} = m,\, (x - x_{0})[/tex].
For the line in this question, the slope is [tex]m = 1[/tex]. Take [tex](5,\, 6)[/tex] as the chosen point on this line. The point-slope form equation of this line would be:
[tex]y - 6 = (x - 5)[/tex].
Rewrite to obtain the equation of this line in the slope-intercept form:
[tex]y = x + 1[/tex].