Question

write an equation in point slope form to represent this graph. $y - y_1 = m(x - x_1)$

Explanation:

Step1: Find two points on the line

From the graph, we can see that the line passes through \((0,1)\) (the y - intercept) and \((1, - 1)\). We can also use \((0,1)\) and \((0.5,0)\) or other pairs of points. Let's use \((x_1,y_1)=(0,1)\) and \((x_2,y_2)=(1, - 1)\).

Step2: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the values \(y_2=-1\), \(y_1 = 1\), \(x_2 = 1\), \(x_1=0\) into the formula, we get \(m=\frac{-1 - 1}{1 - 0}=\frac{-2}{1}=-2\).

Step3: Write the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\). We can use the point \((0,1)\) (so \(x_1 = 0\) and \(y_1=1\)) and the slope \(m=-2\). Substituting these values into the formula, we get \(y - 1=-2(x - 0)\), which simplifies to \(y - 1=-2x\) (but we can also leave it in the point - slope form as \(y - 1=-2(x - 0)\)). We could also use other points on the line, for example, if we use the point \((1,-1)\) with \(m = - 2\), the equation would be \(y+1=-2(x - 1)\).

Answer:

\( y - 1 = -2(x - 0) \) (or other valid point - slope form equations using points on the line, e.g., \( y - 0=-2(x - 0.5) \), but using the y - intercept \((0,1)\) and slope \(-2\) is straightforward)