Lesson Example Discussion Quiz: Class Homework |
Step-5 |
Title: Linear Functions |
Grade: 1300-a Lesson: S1-L3 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
Lesson Steps
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
Find an equation of the linear function given f(-2) = 9 and f(5) = 3. |
|
2 |
Step |
Given functions are |
f(-2) = 9 and f(5) = 3 |
3 |
Formula: |
To find the equation of a linear function, we can use the point-slope form of a linear equation |
\$"y" - "y"_1 = "m"("x" - "x"_1)\$ |
4 |
Formula: |
Slope |
\$"m" = ("y"_2 - "y"_1) / ("x"_2 - "x"_1)\$ |
5 |
Step |
Here the points are |
\$ ("x"_1, "y"_1)\$ = (- 2, 9) and \$("x"_2, "y"_2) = (5, 3)\$ |
6 |
Step |
Plug the value in the slope formula |
\$"m" = (3 - 9)/(5 - (-2)) \$ \$"m" = - 6/7 \$ |
7 |
Step |
Let’s use the point \$(x_1, y_1)\$ |
(-2, 9) |
8 |
Step |
Now plug the value in the point-slope formula |
\$"y" - 9 = (- 6/7)("x" - (- 2))\$ \$"y" - 9 = (- 6/7)("x" + 2)\$ \$"y" - 9 = (- 6/7)"x" - (12/7)\$ |
9 |
Step |
Multiply 7, then simplify |
7(y - 9) = - 6x - 12 7y - 63 = - 6x - 12 \$"y" = -(6"x")/7 + (51)/7\$ |
10 |
Step |
So,therefore the equation of the linear function is \$ "f"("x") = (- 6"x")/7 + (51)/7\$. |
|
11 |
Choice.A |
This is correct because it done accurately done the calculation by using the formula |
\$ "y" = (- 6"x")/7 + (51)/7\$ |
12 |
Choice.B |
The sign before the \$51/7\$ term is incorrect. It should be positive because the y-intercept we found is positive. So, option B is not correct |
\$ "y" = (-6/7)"x" - 51/7\$ |
13 |
Choice.C |
\$"f"("x") = (6/7)"x" + 51/7\$, is inaccurate due to its positive slope contrary to the function’s decrease |
\$"y" = (6/7)"x" + 51/7\$ |
14 |
Choice.D |
\$"y" = (6/7)"x" − 51/7\$, has the wrong sign in front of the constant term, it’s negative instead of positive |
\$"y" = (6/7)"x" - 51/7\$ |
15 |
Answer |
Option |
A |
16 |
Sumup |
Can you summarize what you’ve understood in the above steps? |
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