find the equation of the line passing through the points (1,-5) and (9,11).\ny = ?x +

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through 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, $x_1 = 1,y_1=-5,x_2 = 9,y_2 = 11$. So $m=\frac{11-(-5)}{9 - 1}=\frac{11 + 5}{8}=\frac{16}{8}=2$.

Step2: Find the y - intercept

Use the point - slope form $y-y_1=m(x - x_1)$ and then convert it to slope - intercept form $y=mx + b$. Let's use the point $(1,-5)$ and $m = 2$. Substitute into $y-y_1=m(x - x_1)$: $y-(-5)=2(x - 1)$, which simplifies to $y + 5=2x-2$. Then solve for $y$: $y=2x-2 - 5$, so $y=2x-7$.

Answer:

$y = 2x-7$