given point with slope

Question

The question is write the standard form of the equation of the line through the given point with the given slope

 

through: (1,2), slope=7

 

Answer 1

Hello, thank you for taking the time to post your question!

The underlying equation that you want to use here is the point-slope form of a linear equation:

y−y1​=m(x−x1​)

For this set of values, we have a slope m=7 and a point (x1​,y1​)=(1,2).

Plugging these values into the point-slope equation gives you: y−2=7(x−1)

Solving that algebraically to put it into the slope-intercept form (y=mx+b) yields:

y−2=7x−7

y=7x−7+2

y=7x−5

To convert this equation to the standard form (Ax+By=C), you need to rearrange the terms: y=7x−5 −7x+y=−5

Multiplying the entire equation by -1 to make the coefficient of x positive gives: 7x−y=5

Meaning that the standard from of the equation of the line for these parameters is 7x - y = 5.

Answer 2

Stacy I always use Mx+b=y

so since we know where the line goes through

write

7x+b=y and we know x and y coordinates so put them in equation to solve for b

or 7(x) or 7*(1)

7+b=2 or B=-5

the equation of the line is

7x-5= y