What is the y intercept of the following graph given the points (1,2)(7,-2) 8/3 5 -1 -2/3

## Step 1: Calculate the slope<br />### The slope ($m$) is calculated using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the given points $(1,2)$ and $(7,-2)$, we get $m = \frac{-2 - 2}{7 - 1} = \frac{-4}{6} = -\frac{2}{3}$.<br /><br />## Step 2: Determine the equation of the line<br />### Using the point-slope form $y - y_1 = m(x - x_1)$ with point $(1,2)$ and slope $m = -\frac{2}{3}$, the equation becomes $y - 2 = -\frac{2}{3}(x - 1)$. Simplifying this gives $y = -\frac{2}{3}x + \frac{2}{3} + 2$, which further simplifies to $y = -\frac{2}{3}x + \frac{8}{3}$.<br /><br />## Step 3: Find the y-intercept<br />### The y-intercept is the value of $y$ when $x = 0$. Substituting $x = 0$ into the equation $y = -\frac{2}{3}x + \frac{8}{3}$, we get $y = \frac{8}{3}$.