Question

write the standard form of the equation of the line through the given point with the given slope THROUGH:(1,2), slope =7, 50 POINTS

Answer 1

A standard equation for a line is usually written as y=mx+b, m being the slope and b the y-intercept. We already have the slope, 7. To find the y-intercept we need to make an equation. The coordinates (1,2) will help us. We can plug the x from our point into the equation as well as our y. 1 is the x and 2 is the y. Therefore our equation is 2=7(1)+b. Now we solve. 7×1=7, so 2=7+b. Then we subtract 7 from both sides to get rid of the 7 on the right side. In addition, the 7 is positive so subtracting will get rid of it.
2=7+b
-7 -7
2-7 is -5. Therefore -5 is b.
Now we can make an equation.
y will remain y.
x will remain x.
m = 7
b = -5
y=7x+(-5) or y=7x-5

I hope this helped! (:

Answer 2

Answer:

7 x − 1 y = 5

Explanation:

First, we can write the equation in point-slope form. The point-slope formula states:  

( y − y 1 ) = m ( x − x 1 )

Where  

m  is the slope and  ( x 1  y 1 )

is a point the line passes through.

Substituting the values from the problem gives:

( y − 2 ) = 7 ( x − 1 )

Now, we need to convert to standard form. The standard form of a linear equation is:  

A x + B y = C

where, if at all possible,  A ,  B , and  C  are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

We convert as follows:

y − 2 = ( 7 × x ) − ( 7 × 1 )

y − 2 = 7 x − 7

− 7 x + y − 2 + 2 = − 7 x + 7 x − 7 + 2

− 7 x + y − 0 = 0 − 5

− 7 x + y = − 5

− 1 ( − 7 x + y ) = − 1 × − 5

( − 1 × − 7 x ) + ( − 1 × y ) = 5

7 x − 1 y = 5