To find the equation of the line passing through the points [tex]\((0, 4)\)[/tex] and [tex]\((-2, 3)\)[/tex], we need to determine the slope and the y-intercept of the line.
### Step 1: Calculate the Slope
The slope [tex]\(m\)[/tex] of a line through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the given points [tex]\((0, 4)\)[/tex] and [tex]\((-2, 3)\)[/tex]:
[tex]\[
m = \frac{3 - 4}{-2 - 0} = \frac{-1}{-2} = 0.5
\][/tex]
### Step 2: Find the Y-Intercept
The equation of a line in slope-intercept form is:
[tex]\[
y = mx + b
\][/tex]
where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept. We can use one of the points to find the y-intercept. Using the point [tex]\((0, 4)\)[/tex]:
[tex]\[
4 = 0.5 \cdot 0 + b
\][/tex]
This simplifies to:
[tex]\[
b = 4
\][/tex]
### Step 3: Write the Equation of the Line
Now that we have the slope [tex]\(m = 0.5\)[/tex] and the y-intercept [tex]\(b = 4\)[/tex], we can write the equation of the line as:
[tex]\[
y = 0.5x + 4
\][/tex]
So the equation of the line passing through the points [tex]\((0, 4)\)[/tex] and [tex]\((-2, 3)\)[/tex] is:
[tex]\[
y = 0.5x + 4
\][/tex]
