What is the standard form of a linear equation whose graph passes through (3,-5) with a slope of 2/3

Question

What is the standard form of the linear equatio whose graph passes through (3,-5) with a slope of 2/3

Answer 1

Hi Elizabeth, the standard form of a line is: Ax + By = C. To find the solution to your problem, start with the point-slope form of a line.

 

Point-slope form of a line:

 

y - y₁ = m * (x - x₁)

 

Where:

 

m is the given slope.

 

(x₁, y₁) is the given point.

 

y - (-5) = 2/3 * (x - 3)

 

y + 5 = 2/3 * (x - 3)

 

Multiply entire equation by 3 to clear fraction:

 

3y + 15 = 2 * (x - 3)

 

Clear parenthesis:

 

3y + 15 = 2x - 6

 

Put in standard form of the line:

 

Subtract 2x from both sides:

 

-2x + 3y + 15 = -6

 

Subtract 15 from both sides:

 

-2x + 3y = -21

 

Multiply entire equation by -1:

 

2x - 3y = 21

 

This is the standard form.

 

Questions?