To find the equation of a line that passes through the point [tex]\((4, 3)\)[/tex] and has a slope of [tex]\(2\)[/tex], we can use the point-slope form of the line equation:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where:
- [tex]\((x_1, y_1)\)[/tex] is a point on the line
- [tex]\(m\)[/tex] is the slope
Substituting the given point [tex]\((4, 3)\)[/tex] and the slope [tex]\(2\)[/tex] into the point-slope form, we get:
[tex]\[ y - 3 = 2(x - 4) \][/tex]
Next, we simplify this equation to get it into slope-intercept form [tex]\(y = mx + b\)[/tex]:
1. Distribute the [tex]\(2\)[/tex]:
[tex]\[ y - 3 = 2x - 8 \][/tex]
2. Add [tex]\(3\)[/tex] to both sides to isolate [tex]\(y\)[/tex]:
[tex]\[ y = 2x - 8 + 3 \][/tex]
[tex]\[ y = 2x - 5 \][/tex]
So, the equation of the line is:
[tex]\[ y = 2x - 5 \][/tex]
Given the options:
- [tex]\( y = 2x - 11 \)[/tex]
- [tex]\( y = 2x - 7 \)[/tex]
- [tex]\( y = 2x - 5 \)[/tex]
- [tex]\( y = 2x - 1 \)[/tex]
The correct answer is:
[tex]\[ y = 2x - 5 \][/tex]
