find an equation of the line with the given slope that passes through the given point

Question

M=7,(6,6)

The equation of the line in the form Ax+By=C is 

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−y_1=m(x−x_1)

For this set of values, we have a slope m=7 and a point (x_1,y_1) = (6,6).

Plugging these values into the point-slope equation gives you: y−6=7(x−6)

Solving that algebraically for the value of “y” to put it into the slope-intercept form (y=mx+b) yields: y−6=7x−42

y=7x−42+6

y=7x−36

To convert this equation to the form Ax+By=C, you need to rearrange the terms:

y=7x−36

−7x+y=−36

Multiplying the entire equation by -1 to make the coefficient of x positive gives: 7x−y=36

Meaning that the equation of the line in the form Ax+By=C is 7x−y=36.

Answer 2

The point-slope equation for a line is

 

y - y0 = m(x - x0). Since you're given m = 7, and (x0, y0) = (6, 6), plug those values in and put the x- and y- terms on the left side and the constant on the right side.