Let's analyze the given equation [tex]\( y - 4 = 5(x - 2) \)[/tex] to determine the slope and a point on the line.
The equation is provided in the point-slope form:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\((x_1, y_1)\)[/tex] is a point on the line.
1. Identify the slope [tex]\(m\)[/tex]:
In the equation [tex]\( y - 4 = 5(x - 2) \)[/tex], the coefficient of [tex]\( (x - 2) \)[/tex] is 5. Therefore, the slope [tex]\(m\)[/tex] is 5.
2. Identify the point [tex]\((x_1, y_1)\)[/tex]:
Observing the equation [tex]\( y - 4 = 5(x - 2) \)[/tex], it is evident that the point on the line is where [tex]\( x_1 = 2 \)[/tex] and [tex]\( y_1 = 4 \)[/tex].
Therefore, the point [tex]\((x_1, y_1)\)[/tex] is [tex]\((2, 4)\)[/tex].
Now let's compare these results with the given options:
A. The slope is 5 and [tex]\((2,4)\)[/tex] is on the line.
B. The slope is 4 and [tex]\((2,5)\)[/tex] is on the line.
C. The slope is 2 and [tex]\((5,4)\)[/tex] is on the line.
D. The slope is 5 and [tex]\((-2,-4)\)[/tex] is on the line.
The correct answer is:
A. The slope is 5 and [tex]\((2,4)\)[/tex] is on the line.
