Math question !

Question

Which equation in standard form represents the line that passes through the points (–3, 7) and (4, 10)?

Answer 1

To find the equation of the line going between the points (–3, 7) and (4, 10), first find the slope using the slope equation m = (y₂ - y₁)/(x₂ - x₁) where x₁ = -3, y₁ = 7, x₂ = 4, and y₂ = 10:

m = (10 - 7)/(4 - -3) = 3/7

Then use the slope you calculated above and one of the points, I'll choose (4, 10) and plug them into the point-slope form of a line: y - y₁ = m(x - x₁) where "m" is the slope and (x₁, y₁) is the point (meaning x₁ = 4 and y₁ = 10). Note that this x₁ and y₁ have nothing to do with the x₁ and y₁ you used in step 1 to calculate slope.

y - y₁ = m(x - x₁)

y - 10 = (3/7)(x - 4)

y - 10 = (3/7)x - 12/7

y = (3/7)x - 12/7 + 10

y = (3/7)x - 12/7 + 70/7

y = (3/7)x + 58/7

Multiply both sides by 7 to get:

7y = 3x + 58

subtract 7y from both sides to get:

0 = 3x - 7y + 58

subtract 58 from both sides to get:

3x - 7y = -58