To write the equation of the line passing through the points [tex]\((-5,6)\)[/tex] and [tex]\((5,4)\)[/tex], follow these steps:
1. Find the slope [tex]\( m \)[/tex]:
The slope of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is calculated using the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the given points [tex]\((-5, 6)\)[/tex] and [tex]\((5, 4)\)[/tex]:
[tex]\[
m = \frac{4 - 6}{5 - (-5)} = \frac{-2}{10} = -0.2
\][/tex]
2. Find the y-intercept [tex]\( b \)[/tex]:
To find the y-intercept, use the slope-point form of the line equation:
[tex]\[
y = mx + b
\][/tex]
Substituting one of the points, say [tex]\((-5, 6)\)[/tex], and the slope [tex]\( m = -0.2 \)[/tex]:
[tex]\[
6 = -0.2(-5) + b
\][/tex]
Simplify the expression:
[tex]\[
6 = 1 + b \implies b = 6 - 1 = 5
\][/tex]
3. Write the equation of the line:
With [tex]\( m = -0.2 \)[/tex] and [tex]\( b = 5 \)[/tex], the equation of the line in slope-intercept form [tex]\( y = mx + b \)[/tex] is:
[tex]\[
y = -0.2x + 5
\][/tex]
Thus, the equation of the line passing through the points [tex]\((-5, 6)\)[/tex] and [tex]\((5, 4)\)[/tex] is:
[tex]\[
y = -0.2x + 5
\][/tex]
