(A) Find the slope of the line that passes through the givin points.
(B) Find the poinlslope form of the equation of the line.
© Find the slope-intercept form of the equation of the line
(D) Find the slandard form of the equation of the line.
( ) and ( 1,4 )
(A) Select the correct choice below and, il necessary, fill in the answer box to complete your choico.
A. (Type an integer or a simplified fraction.)
B. The slope is not defined
(B) What is the equation of the line in point-slope form? Select the correct choice below and, if necessary, fil in the answer box lo complete your choice.
A. (Simplify your answer. Use integors or fractions for any numbors in the equation.)
B. There is no point-slope form

Ask by Haynes Munoz. in the United States

Jan 21,2025

Question

(A) Find the slope of the line that passes through the givin points.
(B) Find the poinlslope form of the equation of the line.
© Find the slope-intercept form of the equation of the line
(D) Find the slandard form of the equation of the line.
( ) and ( 1,4 )
(A) Select the correct choice below and, il necessary, fill in the answer box to complete your choico.
A. (Type an integer or a simplified fraction.)
B. The slope is not defined
(B) What is the equation of the line in point-slope form? Select the correct choice below and, if necessary, fil in the answer box lo complete your choice.
A. (Simplify your answer. Use integors or fractions for any numbors in the equation.)
B. There is no point-slope form

Ask by Haynes Munoz. in the United States

Jan 21,2025

UpStudy AI · Accepted Answer

Let's work through each part of the problem step by step.

### Given Points:
$$
(-5, 4) \quad \text{and} \quad (1, 4)
$$

### (A) Find the Slope of the Line

The **slope** $$ m $$ of a line passing through two points $$ (x_1, y_1) $$ and $$ (x_2, y_2) $$ is calculated using the formula:
$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

Plugging in the given points:
$$
m = \frac{4 - 4}{1 - (-5)} = \frac{0}{6} = 0
$$

**Answer for (A):**
- **Choice A:** $$ m = 0 $$

### (B) Find the Point-Slope Form of the Equation

The **point-slope form** of a line is given by:
$$
y - y_1 = m(x - x_1)
$$
where $$ m $$ is the slope and $$ (x_1, y_1) $$ is a point on the line.

Using the slope $$ m = 0 $$ and one of the points, say $$ (-5, 4) $$:
$$
y - 4 = 0(x - (-5)) \
y - 4 = 0 \cdot (x + 5) \
y - 4 = 0 \
y = 4
$$

**Answer for (B):**
- **Choice A:** $$ y = 4 $$

### (C) Find the Slope-Intercept Form of the Equation

The **slope-intercept form** is:
$$
y = mx + b
$$
where $$ m $$ is the slope and $$ b $$ is the y-intercept.

Using $$ m = 0 $$ and knowing that $$ y = 4 $$ for all points on the line:
$$
y = 0x + 4 \
y = 4
$$

**Answer for (C):**
$$
y = 4
$$

### (D) Find the Standard Form of the Equation

The **standard form** of a line is:
$$
Ax + By = C
$$
where $$ A $$, $$ B $$, and $$ C $$ are integers, and $$ A $$ is non-negative.

From $$ y = 4 $$:
$$
0x + 1y = 4
$$
Simplifying:
$$
y = 4
$$

**Answer for (D):**
$$
y = 4
$$

### Summary of Answers:
- **(A)** Choice **A**: $$ m = 0 $$
- **(B)** Choice **A**: $$ y = 4 $$
- **(C)** Slope-intercept form: $$ y = 4 $$
- **(D)** Standard form: $$ y = 4 $$
- **(A)** The slope $$ m = 0 $$. - **(B)** The point-slope form is $$ y = 4 $$. - **(C)** The slope-intercept form is $$ y = 4 $$. - **(D)** The standard form is $$ y = 4 $$.

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