(A) Find the sope of the line thal passos through tho given points (B) Find the pont stope form of the equation of the hine. (C) Find the stope interment form of the oquation of tho line (D) Find the standard form of the equation of tho lino \( (-5,4) \) and \( (1,4) \) (A) Select the correct chorce be ow and, if necessary, fill in the answer box to complete your choice. A. \( m=0 \) (Typo an integer or a simplified fraclion.) B. The slope is not delined (B) What is the equation of the line in point-slope form? Seloct the correct choice below and, if necossary, fil in the answer box to complete your choice. A. \( y-4=0^{\circ} \) (Simplify your answer. Use integers or fractions for any numbers in the equation.) B. There is no point-slope lom. (C) What is the equation of the line in slope-intercept form? Select the correcl choico below and, if necessary, fall in the answer box to complete your choice. A. \( \square \) (Simplify your answer. Use inlegers or fractions for any numbers in the equation.) B. Thore is no slope-intercepl form.

Let's solve each part of the problem step by step using the given points \((-5, 4)\) and \( (1, 4) \). ### **(A) Find the Slope of the Line** **Formula for Slope (\(m\)):** \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] **Substituting the Given Points:** \[ m = \frac{4 - 4}{1 - (-5)} = \frac{0}{6} = 0 \] **Correct Choice:** **A. \( m = 0 \)** --- ### **(B) Find the Point-Slope Form of the Equation of the Line** **Point-Slope Form:** \[ y - y_1 = m(x - x_1) \] Using the slope \(m = 0\) and point \((-5, 4)\): \[ y - 4 = 0(x + 5) \quad \Rightarrow \quad y - 4 = 0 \] **Correct Choice:** **A. \( y - 4 = 0 \)** --- ### **(C) Find the Slope-Intercept Form of the Equation of the Line** **Slope-Intercept Form:** \[ y = mx + b \] Substituting \(m = 0\) and using one of the points to find \(b\): \[ y = 0x + 4 \quad \Rightarrow \quad y = 4 \] **Correct Choice:** **A. \( y = 4 \)** --- ### **(D) Find the Standard Form of the Equation of the Line** **Standard Form:** \[ Ax + By = C \] where \(A\), \(B\), and \(C\) are integers, and \(A \geq 0\). Starting from the slope-intercept form \(y = 4\): \[ 0x + y = 4 \] Simplifying, the standard form is: \[ y = 4 \] **Standard Form:** \[ 0x + y = 4 \quad \text{or simply} \quad y = 4 \] --- ### **Summary of Answers:** - **(A)** **A. \( m = 0 \)** - **(B)** **A. \( y - 4 = 0 \)** - **(C)** **A. \( y = 4 \)** - **(D)** **Standard Form:** \( y = 4 \)