Certainly! To find the equation of the line passing through the points [tex]\((-4, 2)\)[/tex] and [tex]\((0, -3)\)[/tex], we can follow these steps:
1. Calculate the slope (m) of the line:
The slope 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]
Using the points [tex]\((-4, 2)\)[/tex] and [tex]\((0, -3)\)[/tex], we have:
[tex]\[
m = \frac{-3 - 2}{0 - (-4)} = \frac{-5}{4} = -1.25
\][/tex]
2. Find the y-intercept (b):
The equation of a line in slope-intercept form is:
[tex]\[
y = mx + b
\][/tex]
We already have the slope [tex]\(m = -1.25\)[/tex]. We can use one of the points to find the y-intercept [tex]\(b\)[/tex]. Let's use the point [tex]\((0, -3)\)[/tex]:
[tex]\[
-3 = -1.25(0) + b \Rightarrow b = -3
\][/tex]
3. Write the equation of the line:
Now that we have the slope [tex]\(m = -1.25\)[/tex] and the y-intercept [tex]\(b = -3\)[/tex], we can write the equation of the line as:
[tex]\[
y = -1.25x - 3
\][/tex]
Therefore, the equation of the line passing through the points [tex]\((-4, 2)\)[/tex] and [tex]\((0, -3)\)[/tex] is:
[tex]\[
\boxed{y = -1.25x - 3}
\][/tex]
