The equation of the line that is parallel to the graph of y=1/2x+6 and whose y-intercept is -2 is [tex]y = \frac{1}{2}x - 2[/tex]
Solution:
Given that line that is parallel to the graph of [tex]y=\frac{1}{2}x+6[/tex] and whose y-intercept is -2
We have to find the equation of line
The slope intercept form is given as:
y = mx + c ---- eqn 1
where "m" is the slope of line and "c" is the y-intercept
Let us first find slope of line
Given equation of line is:
[tex]y=\frac{1}{2}x+6[/tex] ------- eqn 2
On comparing eqn 1 and eqn 2,
[tex]m = \frac{1}{2}[/tex]
We know that slopes of parallel lines are equal
so the slope of line parallel to given line is also [tex]m = \frac{1}{2}[/tex]
Now let us find the equation of line with slope [tex]m = \frac{1}{2}[/tex] and y - intercept is -2
Substitute [tex]m = \frac{1}{2}[/tex] and c = -2 in eqn 1
[tex]y = \frac{1}{2}x - 2[/tex]
Thus the required equation of line is found
