What is the equation of the straight line shown below? Give your answer in the form $y=m x+c$, where $m$ and $c$ are integers or fractions in their simplest forms.
Solution
Step 1 ：First, we need to find the slope (m) of the line. We can do this by finding the difference in y-coordinates divided by the difference in x-coordinates for any two points on the line. Let's use the points (0, 2) and (1, 0).
Step 2 ：The slope is given by m = \(\frac{y_2 - y_1}{x_2 - x_1}\) = \(\frac{0 - 2}{1 - 0}\) = \(-2\)
Step 3 ：Now that we have the slope, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). Let's use the point (0, 2) to find the equation of the line.
Step 4 ：Plugging in the values, we get y - 2 = -2(x - 0).
Step 5 ：Simplifying the equation, we get y = -2x + 2.
Step 6 ：So the equation of the line is \(y = -2x + 2\), and the values of m and c are -2 and 2, respectively.
Step 7 ：Therefore, the final answer is \(\boxed{-2x + 2}\)
