Question

Write the equation of the line that passes through (4,-3) & (3,0)
m =
b =
y =

Answer 1

m = -3

b = 9

y = -3x + 9

Explanation:

Let us solve the question

∵ The line passes through points (4, -3) and (3, 0)

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

∵ (x1, y1) and (x2, y2) are 2 points on the line

∴ x1 = 4 and y1 = -3

∴ x2 = 3 and y2 = 0

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

∵ m =
`(0--3)/(3-4)` =
`(0+3)/(-1)` = -3

∴ m = -3

∵ The form of the equation of the line is y = m x + b

→ Substitute the value of m in the form of the equation.

∴ y = -3x + b

→ To find b substitute x and y by the coordinates of the point (3, 0) or (4, -3)

∵ x = 3 and y = 0

∴ 0 = -3(3) + b

∴ 0 = -9 + b

→ Add 9 to both sides

∴ 9 = b

∴ b = 9

→ Substitute the value of b in the equation

∵ y = -3x + 9

∴ The equation of the line is y = 3x + 9