Answer:
[tex] y = \dfrac{1}{2}x+ \dfrac{5}{2}[/tex]
Step-by-step explanation:
To write the equation of a line using the point-slope formula, we'll use the given point [tex](-5, 0)[/tex] and slope [tex]m = \dfrac{1}{2}[/tex].
The point-slope formula is:
[tex] \large\boxed{\boxed{ 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 of the line
Given point [tex] (-5, 0) [/tex] and slope [tex] m = \dfrac{1}{2} [/tex], we substitute these values into the formula:
[tex] y - 0 = \dfrac{1}{2}(x - (-5)) [/tex]
Simplify:
[tex] y = \dfrac{1}{2}(x + 5) [/tex]
[tex] \boxed{y = \dfrac{1}{2}x + \dfrac{5}{2}} [/tex]
This is the equation of the line passing through [tex](-5, 0)[/tex] with a slope of [tex] \dfrac{1}{2} [/tex] in slope-intercept form.
