Question

write the point - slope form of the lines equation satisfying the given conditions. then use the point - slope form of the equation to write the slope - intercept form of the equation.
passing through (- 6, 3) and (5, 3)
what is the point - slope form of the equation of the line?
(do not simplify. use integers or fractions for any numbers in the equation.)
what is the slope - intercept form of the equation of the line?
y = 3
(simplify your answer. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, the points are \((-6, 3)\) and \((0, 3)\). So, \( m=\frac{3 - 3}{0 - (-6)}=\frac{0}{6} = 0 \).

Step2: Write the point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((-6, 3)\) (we could also use \((0, 3)\)). Substituting \( m = 0 \), \( x_1=-6 \) and \( y_1 = 3 \) into the point - slope formula, we get \( y - 3=0(x+6) \) (or using the point \((0,3)\), \( y - 3=0(x - 0) \)).

Step3: Derive the slope - intercept form

The slope - intercept form is \( y=mx + b \), where \( b \) is the y - intercept. Since the line passes through \((0, 3)\), the y - intercept \( b = 3 \), and the slope \( m = 0 \). So, substituting into \( y=mx + b \), we get \( y=0x+3=y = 3 \).

Answer:

• Point - slope form: \( y - 3=0(x + 6) \) (or \( y - 3=0(x - 0) \))
• Slope - intercept form: \( y = 3 \)