Answer:
y = 3x + 6
Step-by-step explanation:
We are given a line.
We know this line is parallel to the line y=3x+2, and passes through (1, 9).
We want find the equation of this line.
Parallel lines have the same slopes.
So, let's find the slope of y=3x+2.
The line is written the format y=mx+b, where m is the slope and b is the value of y at the y intercept.
As 3 is in the place of where m (the slope) is, the slope of the line is 3.
It is also the slope of the line parallel to it.
We should write the equation of the line parallel y=3x+2 in slope-intercept form as well, however, before we do that, we can write the line in point-slope form, and then convert it to slope-intercept form.
Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is a point.
We can substitute 3 as m in the formula, as we know that is the slope of the line
[tex]y-y_1=3(x-x_1)[/tex]
Recall that we were given the point (1, 9), which also belongs to (it passes through) the line.
Therefore, we can use its values in the formula.
Substitute 1 as [tex]x_1[/tex] and 9 as [tex]y_1[/tex].
y - 9 = 3(x-1)
We can now convert the equation into slope intercept form.
Notice how y is by itself in slope-intercept form; this means we'll need to solve the equation for y.
Start by distributing 3 to both x and -1.
y - 9 = 3x - 3
Now add 9 to both sides.
y = 3x + 6
