The equation of a line in the slope intercept form is expressed as
y = mx + c
Where
m represents slope
c represents y intercept
The given equation is
y = 3x + 6
If we compare the given equation with the slope intercept equation, we can see that slope = 3
If two lines are parallel, it means that they ahve the same slope. Thus, the slope of the line
that passes through the point (4,7) is 3
We would find it's y intercept, c by substituting m = 3, x = 4 and y = 7 into the slope intercept equation. It becomes
7 = 3 * 4 + c
7 = 12 + c
c = 7 - 12
c = - 5
Thus, we would substitute m = 3 and c = - 5 into the slope intercept equation to get the equation of the line. Thus, we have
y = 3x - 5