Hello!
The answer is:
The standard form of a line that includes the point (22,12) and has a slope of 4, is:
[tex]-4x+y=-76[/tex]
Why?
To solve this problem, we need to remember the standard form of the line which is:
[tex]Ax+By=c[/tex]
So, we are asked to find and write the equation of a line that includes the point (22,12) and has a slope of 4 (positive), in standard form. We know that the slope of a line is the coefficient of the linear term "x".
We need to write the equation in the point-slope form in order to find the standard form.
The point-slope form of the line is equal to:
[tex]y-y_{1}=m(x-x_{1})[/tex]
We are given the point (22,12) and slope of 4.
Where,
[tex]x_{1}=22\\y_{1}=12[/tex]
Then, substituting the given information into the point-slope equation, we have:
[tex]y-12=4(x-22)\\\\y-12=4x-88\\\\y-4x=-88+12\\\\-4x+y=-76[/tex]
So, the correct answer is the last option, the standard form of a line that incluides the point (22,12) and has a slope of 4, is:
[tex]-4x+y=-76[/tex]
Have a nice day!
