Question

Input the equation of the given line in standard form. The line including the two points (5, 3), (8, -2).?
Help on how to find the answer?

Answer 1

first find the slope using the points given and the slope formula
slope(m) = (y2 - y1) / (x2 - x1)
(5,3)...x1 = 5 and y1 = 3
(8,-2)...x2 = 8 and y2 = -2
now we sub
slope(m) = (-2 - 3) / (8 - 5)
slope(m) = -5/3

now that we know the slope, we need the y intercept...that can be found by using the formula y = mx + b and either of your sets of points.
y = mx + b
slope(m) = -5/3
(5,3)...x = 5 and y = 3
now we sub and solve for b, your y intercept
3 = -5/3(5) + b
3 = -25/3 + b
3 + 25/3 = b -- common denominator is 3
9/3 + 25/3 = b
34/3 = b

so our equation is : y = -5/3 + 34/3
However, we need it in standard form Ax + By = C

y = -5/3x + 34/3 -- multiply by the common denominator 3
3y = -5x + 34 -- add 5x to both sides
5x + 3y = 34 <== standard form