To convert the equation [tex]\( x + y = 16 \)[/tex] into slope-intercept form, we need to express the equation in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Step 1: Isolate [tex]\( y \)[/tex] on one side of the equation.
Starting with:
[tex]\[ x + y = 16 \][/tex]
Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[ y = -x + 16 \][/tex]
Now, we have the equation in slope-intercept form:
[tex]\[ y = -x + 16 \][/tex]
Step 2: Identify the slope and the y-intercept.
In the slope-intercept form [tex]\( y = mx + b \)[/tex]:
- The coefficient of [tex]\( x \)[/tex] is the slope ([tex]\( m \)[/tex]).
- The constant term is the y-intercept ([tex]\( b \)[/tex]).
From the equation [tex]\( y = -x + 16 \)[/tex]:
- The slope ([tex]\( m \)[/tex]) is [tex]\(-1\)[/tex].
- The y-intercept ([tex]\( b \)[/tex]) is [tex]\( 16 \)[/tex].
The y-intercept as an ordered pair is [tex]\( (0, 16) \)[/tex].
Summary:
- The equation in slope-intercept form is:
[tex]\[ y = -x + 16 \][/tex]
- The slope of the line is:
[tex]\[ -1 \][/tex]
- The y-intercept of the line is:
[tex]\[ (0, 16) \][/tex]
