Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Match each of the following equations according to their slope and [tex]\( y \)[/tex]-intercept.

[tex]\[
\begin{align*}
1. & \ y = -3x + 4 \\
2. & \ y = 7 \\
3. & \ y = 15x - 7 \\
4. & \ y = -1.5x - 4 \\
5. & \ y = 3x \\
\end{align*}
\][/tex]

[tex]\[
\begin{align*}
A. & \ m = 1.5, \ b = -7 \\
B. & \ m = 0, \ b = 7 \\
C. & \ m = 3, \ b = 0 \\
D. & \ m = -1.5, \ b = -4 \\
E. & \ m = -3, \ b = 4 \\
\end{align*}
\][/tex]

Sagot :

GinnyAnswer
Sure! Let's match the given equations with their respective slopes ([tex]\(m\)[/tex]) and [tex]\(y\)[/tex]-intercepts ([tex]\(b\)[/tex]).

We start by identifying the slope ([tex]\(m\)[/tex]) and [tex]\(y\)[/tex]-intercept ([tex]\(b\)[/tex]) for each equation:

1. [tex]\(y = -3x + 4\)[/tex]
- Slope ([tex]\(m\)[/tex]): -3
- [tex]\(y\)[/tex]-Intercept ([tex]\(b\)[/tex]): 4

2. [tex]\(y = 7\)[/tex]
- Slope ([tex]\(m\)[/tex]): 0 (since there is no [tex]\(x\)[/tex] term, the slope is 0)
- [tex]\(y\)[/tex]-Intercept ([tex]\(b\)[/tex]): 7

3. [tex]\(y = 15x - 7\)[/tex]
- Slope ([tex]\(m\)[/tex]): 15
- [tex]\(y\)[/tex]-Intercept ([tex]\(b\)[/tex]): -7

4. [tex]\(y = -1.5x - 4\)[/tex]
- Slope ([tex]\(m\)[/tex]): -1.5
- [tex]\(y\)[/tex]-Intercept ([tex]\(b\)[/tex]): -4

5. [tex]\(y = 3x\)[/tex]
- Slope ([tex]\(m\)[/tex]): 3
- [tex]\(y\)[/tex]-Intercept ([tex]\(b\)[/tex]): 0 (since no constant term is present, the [tex]\(y\)[/tex]-intercept is 0)

Now we need to match these equations with the given pairs of [tex]\(m\)[/tex] and [tex]\(b\)[/tex]:

1. [tex]\(m = 1.5\)[/tex], [tex]\(b = -7\)[/tex]
- No matching equation, as none of the equations have a slope of 1.5 and [tex]\(y\)[/tex]-intercept of -7.

2. [tex]\(m = 0\)[/tex], [tex]\(b = 7\)[/tex]
- Matching equation: [tex]\(y = 7\)[/tex]

3. [tex]\(m = 3\)[/tex], [tex]\(b = 0\)[/tex]
- Matching equation: [tex]\(y = 3x\)[/tex]

4. [tex]\(m = -1.5\)[/tex], [tex]\(b = -4\)[/tex]
- Matching equation: [tex]\(y = -1.5x - 4\)[/tex]

5. [tex]\(m = -3\)[/tex], [tex]\(b = 4\)[/tex]
- Matching equation: [tex]\(y = -3x + 4\)[/tex]

So, the matched pairs of equations and their slopes and [tex]\(y\)[/tex]-intercepts are:

1. [tex]\(m = 0\)[/tex], [tex]\(b = 7\)[/tex]: [tex]\(y = 7\)[/tex]
2. [tex]\(m = 3\)[/tex], [tex]\(b = 0\)[/tex]: [tex]\(y = 3x\)[/tex]
3. [tex]\(m = -1.5\)[/tex], [tex]\(b = -4\)[/tex]: [tex]\(y = -1.5x - 4\)[/tex]
4. [tex]\(m = -3\)[/tex], [tex]\(b = 4\)[/tex]: [tex]\(y = -3x + 4\)[/tex]

Therefore, the resulting matched equations are:

[tex]\[ y = 7, \quad y = 3x, \quad y = -1.5x - 4, \quad y = -3x + 4 \][/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.