PLEASE HELP its math
1 answer:
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 , where m is the slope and
is a point.
We can substitute 3 as m in the formula, as we know that is the slope of the line
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 and 9 as
.
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.
<u>y = 3x + 6 </u>
You might be interested in
Your calculator's cubic regression function can tell you the equation is
... f(x) = 2x³ + 5x² -12x = x(x +4)(2x-3)
The x-intercepts are -4, 0, +1.5.
_____
If you want to solve this "by hand", you can first of all recognize that since there is an x-intercept at 0, the cubic will only have three coefficients. That is, you can write the equation as
... f(x) = ax³ + bx² + cx
Substituting the given points (except (0, 0)) gives three linear equations in a, b, c.
... -a +b -c = 15 . . . . . for x=-1
... a + b + c = -5 . . . . for x=1
... 8a +4b +2c = 12 . . for x=2
adding the first two equations gives 2b=10, or b=5. Now, you can reduce the system to
... a + c = -10
... 4a +c = -4
Subtracting the first of these equations from the second gives 3a=6, or a=2. That tells you c=-12 (from a+c=10).
Then your equation is
... f(x) = x(2x² +5x -12)
Factoring by any of the usual techniques, or graphing, or using the quadratic formula will tell you the zeros (x-intercepts) are as above.
_____
Since the input values are sequential, you can also develop the function from differences of the output values. Those are 15, 0, -5, 12. First differences are -15, -5, +17. Second differences are +10, +22. The third difference is 12. Using the first of these differences in appropriate places in the interpolating polynomial formula, we have
... f(x) = 15 + (x+1)(-15 + (x)/2·(10 + (x-1)/3·(12))) = 2x³ +5x² -12x . . . . as above
