To find the equation of the line that passes through the points [tex]\((-2, 4)\)[/tex] and [tex]\((2, 0)\)[/tex], we'll follow these steps:
### Step 1: Calculate the Slope (m)
The slope [tex]\( m \)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Plugging in the given points [tex]\((x_1, y_1) = (-2, 4)\)[/tex] and [tex]\((x_2, y_2) = (2, 0)\)[/tex]:
[tex]\[
m = \frac{0 - 4}{2 - (-2)} = \frac{-4}{4} = -1
\][/tex]
### Step 2: Calculate the Y-intercept (b)
The slope-intercept form of a line is:
[tex]\[
y = mx + b
\][/tex]
To find the y-intercept [tex]\( b \)[/tex], we can use either of the given points. Using the point [tex]\((-2, 4)\)[/tex]:
[tex]\[
4 = -1 \cdot (-2) + b \implies 4 = 2 + b \implies b = 4 - 2 = 2
\][/tex]
### Step 3: Form the Equation
Now, with the slope [tex]\( m = -1 \)[/tex] and the y-intercept [tex]\( b = 2 \)[/tex], the equation of the line is:
[tex]\[
y = -x + 2
\][/tex]
### Step 4: Match the Equation with Given Choices
Comparing it to the given choices:
1. [tex]\( y = x - 2 \)[/tex]
2. [tex]\( y = -x + 2 \)[/tex]
3. [tex]\( y = x + 2 \)[/tex]
The correct choice is:
[tex]\[
y = -x + 2
\][/tex]
Hence, the equation of the line that passes through the points [tex]\((-2, 4)\)[/tex] and [tex]\((2, 0)\)[/tex] is:
\[
\boxed{y = -x + 2}
\
