Find the slope and the equation for the line passing through the points: $(1,0)$ and $(0,2)$. a) $m=$ b) The equation for the line:

Step 1 ：Calculate the slope (m) of the line passing through two points using the formula: \(m = \frac{y2 - y1}{x2 - x1}\)

Step 2 ：Substitute the given points (x1, y1) = (1, 0) and (x2, y2) = (0, 2) into the formula: \(m = \frac{2 - 0}{0 - 1} = -2\)

Step 3 ：The equation of a line in slope-intercept form is \(y = mx + b\), where m is the slope and b is the y-intercept

Step 4 ：Substitute m = -2 and one of the points (1, 0) into the equation to find b: \(0 = -2*1 + b\) which simplifies to \(b = 2\)

Step 5 ：Substitute m = -2 and b = 2 into the equation of the line to get the final equation: \(y = -2x + 2\)

Step 6 ：\(\boxed{y = -2x + 2}\) is the final equation of the line