Write the equation of a line in standard form

Question

Slope equal to 2 and passing through (-5,1)

Answer 1

slope intercept form of equation for line:

 

y = mx + b

given:

 

m = 2, x = -5, y = 1

 

1 = 2(-5) + b

 

1 = -10 + b

 

b = 11

 

so equation:

 

y = 2x + 11  equation(1)

 

standard form for equation of line is:

 

Ax + By = C, so we rearrange the equation (1)

 

 

2x  - y = -11

Answer 2

Standard Form of a line is:

Ax + By = C where A is a positive integer, and B, and C are integers.

 

So we have a few conditions we must meet.

 

We can plug those numbers into our slope-intercept equation (Y= M * X + B) where M is the slope and B is the Y-intercept.

 

We will first use the points to solve for B, and then convert that to Standard Form:

 

Solve for B:

 

1 = 2 * (-5) + B

1 - ( 2 * (-5) ) = B

1 + 10 = B = 11

 

Convert to Standard Form:

Y = 2 * X + 11 ; Subtract Y from both sides to keep A positive

0 = 2 * X - Y + 11; Subtract 11 from both sides

-11 = 2X - Y

 

Answer

2X - Y = -11

 

A = 2

B = -1

C = -11

 

The check:

-11 = 2 (-5) - (1) = -11

Answer 3

The standard equation of a line with a slope m and an intercept b is given by the equation

 

y= mx + b

 

However when given only the slope and a point of interception not on the y-axis, we best use the slope intercept formula which is given by;

 

(y-y1)=m(x-x1)

 

where (x1,y1) is the point of intersection and m is the slope. We will substitute and solve for y.

 

y-1 = 2(x-(-5))

y-1 = 2x+10

y = 2x+ 11

 

Therefore the standard form for the equation in question is

y-2x=11

 

Ensure coefficient of x is positive by multiplying the equation by -1(both sides, all terms)

 

2x - y = -11