Sure! Let's solve this problem step-by-step.
### Step 1: Identify the slope [tex]\( m \)[/tex]
The slope [tex]\( m \)[/tex] of the 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]
Given points are [tex]\( M(-3, 5) \)[/tex] and [tex]\( N(2, 0) \)[/tex].
Plugging in these values:
[tex]\[
m = \frac{0 - 5}{2 - (-3)} = \frac{-5}{2 + 3} = \frac{-5}{5} = -1
\][/tex]
So, the slope [tex]\( m = -1 \)[/tex].
### Step 2: Write the equation in point-slope form
The point-slope form of the equation of a line is:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Using point [tex]\( M(-3, 5) \)[/tex] and slope [tex]\( m = -1 \)[/tex]:
[tex]\[
y - 5 = -1(x - (-3))
\][/tex]
Simplify the right-hand side:
[tex]\[
y - 5 = -1(x + 3)
\][/tex]
### Step 3: Simplify the equation and isolate the y variable
Let's distribute [tex]\(-1\)[/tex] on the right-hand side:
[tex]\[
y - 5 = -x - 3
\][/tex]
Now isolate the [tex]\( y \)[/tex] variable:
[tex]\[
y = -x - 3 + 5
\][/tex]
[tex]\[
y = -x + 2
\][/tex]
So the equation of the line [tex]\( MN \)[/tex] is:
[tex]\[
y = -x + 2
\][/tex]
To summarize:
- The slope [tex]\( m = -1 \)[/tex]
- The equation of the line in slope-intercept form is [tex]\( y = -x + 2 \)[/tex]
