Explanation:
Substitute the slope from original line (3 in this case) into the equation of the line
$ y = \red 3 x + b $
Step 2
Substitute the given point (1, 7) into the x and y values
$ y = \red 3 x + b \\ 7 = \red 3 (1) + b $
Step 3
Solve for b (the y-intercept )
$ \begin{align*} 7 &= 3 (1) + b \\ 7 &= 3 + b \\ -3 & -3 \\ \hline \\ 4 &= b \\ \end{align*} $
Step 4
Substitute this value for 'b' in the slope intercept form equation $ y = 3x + 4 $
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Hope it help you