Question

write the slope - intercept form of the equation for the line passing through the given pair of points. (- 8, 1) and (9, 5) \\(\circ\\) \\(y = \frac{5}{4}x + \frac{101}{4}\\) \\(\circ\\) \\(y = -\frac{4}{17}x + \frac{49}{17}\\) \\(\circ\\) \\(y = -\frac{5}{4}x + \frac{101}{4}\\) \\(\circ\\) \\(y = \frac{4}{17}x + \frac{49}{17}\\)

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 \((-8, 1)\) and \((9, 5)\), we have \( x_1=-8,y_1 = 1,x_2=9,y_2 = 5 \). So \( m=\frac{5 - 1}{9-(-8)}=\frac{4}{17} \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((-8,1)\) and \( m = \frac{4}{17} \), we get \( y-1=\frac{4}{17}(x + 8) \).

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y-1=\frac{4}{17}x+\frac{32}{17} \). Then add 1 to both sides. Since \( 1=\frac{17}{17} \), we have \( y=\frac{4}{17}x+\frac{32}{17}+\frac{17}{17}=\frac{4}{17}x+\frac{49}{17} \).

Answer:

\( y=\frac{4}{17}x+\frac{49}{17} \) (the fourth option: \( y=\frac{4}{17}x+\frac{49}{17} \))