Question

write an equation of the line that passes through a pair of points:
a. $y = x + 3$
b. $y = x - 3$
c. $y = -x + 2$
d. $y = -x - 2$

Explanation:

Step1: Identify two points

From the graph, the line passes through \((0, 2)\) (y - intercept) and \((2, 0)\).

Step2: Calculate the slope

The slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \((x_1,y_1)=(0,2)\) and \((x_2,y_2)=(2,0)\), we get \(m=\frac{0 - 2}{2 - 0}=\frac{- 2}{2}=- 1\).

Step3: Use slope - intercept form

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
We know \(m=-1\) and from the point \((0,2)\), the y - intercept \(b = 2\).
So the equation of the line is \(y=-x + 2\).

Answer:

c. \(y=-x + 2\)