To find the equation of the line that passes through the points [tex]\((-12, 11)\)[/tex] and [tex]\((14, -15)\)[/tex] in slope-intercept form [tex]\(y = mx + b\)[/tex], follow these steps:
1. Determine the slope (m):
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]
Plugging in the coordinates of our points [tex]\((-12, 11)\)[/tex] and [tex]\((14, -15)\)[/tex]:
[tex]\[
m = \frac{-15 - 11}{14 - (-12)} = \frac{-15 - 11}{14 + 12} = \frac{-26}{26} = -1
\][/tex]
2. Find the y-intercept (b):
To find the y-intercept [tex]\(b\)[/tex], use the slope-intercept formula [tex]\(y = mx + b\)[/tex] with one of the points. Let's use [tex]\((-12, 11)\)[/tex]:
[tex]\[
11 = -1 \cdot (-12) + b
\][/tex]
[tex]\[
11 = 12 + b
\][/tex]
Solving for [tex]\(b\)[/tex]:
[tex]\[
b = 11 - 12 = -1
\][/tex]
So, the slope [tex]\(m\)[/tex] is [tex]\(-1\)[/tex], and the y-intercept [tex]\(b\)[/tex] is [tex]\(-1\)[/tex].
3. Write the equation:
Substitute the values of [tex]\(m\)[/tex] and [tex]\(b\)[/tex] into the slope-intercept form [tex]\(y = mx + b\)[/tex]:
[tex]\[
y = -1x - 1
\][/tex]
Therefore, the equation of the line in slope-intercept form is:
[tex]\[
y = -x - 1
\][/tex]
