Question

Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution. (1,5) and (-2,3)

Answer 1

The point-point form of a line, the line through (a,b) and (c,d), is

(c-a)(y-b) = (d-b)(x-a)

For us that's

(-2 - 1)(y - 5) = (3 - 5)(x - 1)

-3y + 15 = -2x + 2

Answer: 2x - 3y = -13

Answer 2

2x - 3y = - 13

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

First obtain the equation in slope-intercept form

y = mx + c ( m is the slope and c the y-intercept )

calculate m using the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 5 ) and (x₂, y₂ ) = (- 2, 3 )

m = $\frac{3-5}{-2-1}$ = $\frac{-2}{-3}$= $\frac{2}{3}$

y = $\frac{2}{3}$ x + c ← partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 5 ), then

5 = $\frac{2}{3}$ + c ⇒ c = $\frac{13}{3}$

rearrange the equation into standard form

multiply through by 3

3y = 2x + 13 ( subtract 3y and 13 from both sides )

2x - 3y = - 13 ← in standard form