Find accurate and reliable answers to your questions on IDNLearn.com. Discover prompt and accurate answers from our community of experienced professionals.

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 :

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]