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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]



Answer :

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]

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