Question

What is an equation of the line that passes through the points (3,4) and (−4,−3)? Put your answer in fully reduced form

Answer 1

The equation of the line is y = x + 1

Explanation:

The equation of the line is y = m x + b, where

• m is the slope of the line

• b is the y-intercept

The rule of the slope of the line is m =
`(y2-y1)/(x2-x1)` , where

• (x1, y1) and (x2, y2) are two points on the line

∵ The line passes through points (3, 4) and (-4, -3)

∴ x1 = 3 and y1 = 4

∴ x2 = -4 and y = -3

→ Substitute them in the rule of the slope above to find it

∵ m =
`(-3-4)/(-4-3)` =
`(-7)/(-7)` = 1

∴ m = 1

→ Substitute it in the form of the equation above

∴ y = 1(x) + b

∴ y = x + b

→ To find b substitute x by 3 and y by 4 in the equation

∵ 4 = 3 + b

→ Subtract 3 from both sides

∵ 4 - 3 = 3 - 3 + b

∴ 1 = b

→ Substitute it in the equation

∴ y = x + 1

∴ The equation of the line is y = x + 1