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Finding a parallel line
When lines are parallel, it means that they have the same slope and run alongside each other without ever touching. An equal symbol $$=$$ , for example, is made up of two lines that run parallel to one another.
Let's find the equation of a line parallel to $$y=\frac{1}{2}x+4$$ that runs through the point $$\left(4,1\right)$$. To do this, we can use either the point-slope or slope-intercept formula.

Slope-intercept form:
The slope-intercept form for the equation of a line is $$y=mx+b$$, in which $$y$$ represents the y-coordinate of a point on the line, $$x$$ represents the x-coordinate of the same point on the line, $$m$$ represents the slope of the line, and $$b$$ represents the y-intercept of the line, the point at which the line intersects the graph's y-axis.
Take the given line's slope, $$\frac{1}{2}$$, and plug it in for $$m$$; plug the x-coordinate, $$4$$, in for $$x$$; plug the y-coordinate, $$1$$, in for $$y$$. This gives us $$1=\frac{1}{2}·4+b$$, which simplifies to $$b=-1$$. We can then plug the slope ($$\frac{1}{2}$$) and y-intercept ($$-1$$) into the slope-intercept formula, $$y=mx+b$$, to get the equation of the line, $$y=\frac{1}{2}x-1$$.

Point-slope form:
The point-slope form for the equation of a line is $$y-y_1=m\left(x-x_1\right)$$, in which $$x$$ and $$y$$ represent the x and y-coordinates of a point on the line, $$x_1$$ and $$y_1$$ represent the x and y-coordinates of another point on the line, and $$m$$ represents the slope of the line.
Take the given line's slope, $$\frac{1}{2}$$, and plug it in for $$m$$; plug the x-coordinate, $$4$$, in for $$x_1$$; plug the y-coordinate, $$1$$, in for $$y_1$$. This gives us the equation of the line in point-slope form, $$\left(y-1\right)=\frac{1}{2}\left(x-4\right)$$. Simplifying this further will give us the equation of the line in slope-intercept form.