Sure, let's find the equation of the line that passes through the points [tex]\((-1, 3)\)[/tex] and [tex]\((0, 1)\)[/tex].
1. Identify the coordinates:
- Point 1: [tex]\((x_1, y_1) = (-1, 3)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (0, 1)\)[/tex]
2. Calculate the slope [tex]\(m\)[/tex]:
The slope formula between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Plugging in the values:
[tex]\[
m = \frac{1 - 3}{0 + 1} = \frac{-2}{1} = -2
\][/tex]
3. Find the y-intercept [tex]\(b\)[/tex]:
The y-intercept can be found using the point-slope form of the line equation [tex]\(y = mx + b\)[/tex]. Using point [tex]\((0, 1)\)[/tex], which lies on the y-axis:
[tex]\[
1 = -2 \cdot 0 + b
\][/tex]
Solving for [tex]\(b\)[/tex]:
[tex]\[
b = 1
\][/tex]
4. Write the equation of the line:
Using the slope [tex]\(m = -2\)[/tex] and y-intercept [tex]\(b = 1\)[/tex], the equation of the line is:
[tex]\[
y = -2x + 1
\][/tex]
So, the required equation of the line is:
[tex]\[
y = -2x + 1
\][/tex]
