To find the slope of the line represented by the equation [tex]\( y - 6 = 5(x - 2) \)[/tex], we need to understand the general form of a linear equation.
Linear equations can often be written in the form known as the slope-intercept form:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the y-intercept of the line.
Let's rewrite the given equation into this slope-intercept form.
The equation given is:
[tex]\[ y - 6 = 5(x - 2) \][/tex]
First, we distribute the 5 on the right side:
[tex]\[ y - 6 = 5x - 10 \][/tex]
Next, we isolate [tex]\( y \)[/tex] by adding 6 to both sides:
[tex]\[ y = 5x - 10 + 6 \][/tex]
Simplify the right side:
[tex]\[ y = 5x - 4 \][/tex]
Now, comparing this with the slope-intercept form [tex]\( y = mx + b \)[/tex], we see that the term [tex]\( 5x \)[/tex] corresponds to [tex]\( mx \)[/tex]. Hence, the coefficient of [tex]\( x \)[/tex] in this form is the slope ([tex]\( m \)[/tex]) of the line.
Therefore, the slope [tex]\( m \)[/tex] is:
[tex]\[ m = 5 \][/tex]
So, the slope of the line represented by the equation [tex]\( y - 6 = 5(x - 2) \)[/tex] is:
C. 5
