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? (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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For the points \((-6, 3)\) and \((5, 3)\), we have \( y_2 - y_1 = 3 - 3 = 0 \) and \( x_2 - x_1 = 5 - (-6)=11 \). So \( m=\frac{0}{11}=0 \).

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 \((5, 3)\)). 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 \((5,3)\), \( y - 3=0(x - 5) \)).

Step3: Convert to slope - intercept form

The slope - intercept form is \( y=mx + b \). Starting with \( y - 3=0(x + 6) \), we simplify the right - hand side: \( y-3 = 0 \). Then, add 3 to both sides to get \( y=0x+3 \), which simplifies to \( y = 3 \).

Answer:

• Point - slope form: \( y - 3=0(x + 6) \) (or \( y - 3=0(x - 5) \))
• Slope - intercept form: \( y = 3 \)