Hello.
We have a point that the line passes through:
[tex]\mathrm{(-5,-1)}[/tex]
We also have the line's slope:
[tex]\mathrm{4}[/tex]
Right now, we do not have enough information to write the equation of the line in slope-intercept form. We need to know the slope and the y-intercept. We do know the slope, but we do not know the y-intercept...yet.
We do have enough information to write the line's equation in Point-Slope Form:
[tex]\mathrm{y-y1=m(x-x1)}[/tex]
Plug in the values:
[tex]\mathrm{y-(-1)=4(x-(-5)}[/tex]
[tex]\mathrm{y+1=4(x+5)}[/tex]
Use the Distributive Property (a(b+c)=ab+ac) :
[tex]\mathrm{y+1=4x+20}[/tex]
Move 1 to the right:
[tex]\mathrm{y=4x+20-1}[/tex]
Subtract:
[tex]\mathrm{y=4x+19}[/tex]
Now we have the equation in slope-intercept form.
Therefore, the answer is
[tex]\mathrm{y=4x+19}[/tex]
I hope it helps.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
Answer:
[tex]\displaystyle y = 4x + 19[/tex]
Step-by-step explanation:
Plug the information into the Slope-Intercept Formula like so:
[tex]\displaystyle y = mx + b \\ \\ -1 = 4[-5] + b \hookrightarrow -1 = -20 + b; 19 = b \\ \\ \\ \boxed{y = 4x + 19}[/tex]
I am joyous to assist you at any time.
