To write the equation of the line passing through the points (-5, 6) and (5, 4), we need to determine two things: the slope and the y-intercept.
### Step 1: Calculate the Slope
The slope [tex]\( m \)[/tex] 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]
Here, [tex]\((x_1, y_1) = (-5, 6)\)[/tex] and [tex]\((x_2, y_2) = (5, 4)\)[/tex]. Substituting the values:
[tex]\[ m = \frac{4 - 6}{5 - (-5)} \][/tex]
[tex]\[ m = \frac{4 - 6}{5 + 5} \][/tex]
[tex]\[ m = \frac{-2}{10} \][/tex]
[tex]\[ m = -0.2 \][/tex]
### Step 2: Calculate the Y-Intercept
The slope-intercept form of a line is given by the equation [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept. To find the y-intercept [tex]\( b \)[/tex], we can use one of the given points and substitute [tex]\( x \)[/tex], [tex]\( y \)[/tex], and [tex]\( m \)[/tex] into the equation [tex]\( y = mx + b \)[/tex].
Using the point [tex]\((-5, 6)\)[/tex]:
[tex]\[ 6 = (-0.2)(-5) + b \][/tex]
[tex]\[ 6 = 1 + b \][/tex]
[tex]\[ b = 6 - 1 \][/tex]
[tex]\[ b = 5 \][/tex]
### Step 3: Write the Equation
Now that we have the slope [tex]\( m = -0.2 \)[/tex] and the y-intercept [tex]\( b = 5 \)[/tex], we can write the equation of the line in slope-intercept form:
[tex]\[ y = -0.2x + 5 \][/tex]
Hence, the equation of the line passing through the points (-5, 6) and (5, 4) is:
[tex]\[ y = -0.2x + 5 \][/tex]
