Answer :
Linear Equations
Typically, linear equations are written in slope-intercept form:
[tex]y=mx+b[/tex]
- m = slope
- b = y-intercept (the value of y when the line crosses the y-axis)
To find the equation of a line given a point and the slope:
- Plug the slope into y=mx+b as m
- Plug the point into y=mx+b as (x,y)
- Solve for b
- Plug b back into y=mx+b along with m
Solving the Question
We're given:
- [tex]m=\dfrac{1}{5}[/tex]
- Passes through (-5,-4)
[tex]y=mx+b[/tex]
⇒ Plug in the slope, [tex]\dfrac{1}{5}[/tex]:
[tex]y=\dfrac{1}{5}x+b[/tex]
⇒ Plug in the point (-5,-4) and solve for b:
[tex]-4=\dfrac{1}{5}(-5)+b\\\\-4=-1+b\\\\b=-3[/tex]
⇒ Therefore, the y-intercept of the line is -3. Plug this back into our original equation as b:
[tex]y=\dfrac{1}{5}x-3[/tex]
Answer
[tex]y=\dfrac{1}{5}x-3[/tex]