Maths homework help?

Question

1. What is the equation if the line passes through (0,4) and (3,13) 
2. What is the equation if the line passes through (0.7) and (2,-1)

Answer 1

1).

The points are (0, 4) and (3, 13).

Slope - intercept - form of a line equation : y = mx + b, where, m is slope and b is y - intercept.

Slope (m ) = ( y ₂ - y ₁ ) / ( x ₂ - x ₁ ).

Substitute the values of (x ₁, y ₁) = (0, 4) and (x ₂, y ₂) = (3, 13) in (m ) = ( y ₂ - y ₁ ) / ( x ₂ - x ₁ ).

m = (13 - 4) / (3 - 0) = 9 / 3 = 3.

Substitute the values of (x, y ) = (0, 4) and m = 3 in y = mx + b.

4 = 3(0) + b

⇒ b = 4.

Substitute the values of b = 4 and m = 3 in y = mx + b.

y = 3x + 4.

Therefore, the slope - intercept - form of a line equation is y = 3x + 4.

2).

The points are (0, 7) and (2, - 1).

Slope - intercept - form of a line equation : y = mx + b, where m is slope and b is y - intercept.

Slope (m ) = ( y ₂ - y ₁ ) / ( x ₂ - x ₁ ).

Substitute the values of (x ₁, y ₁) = (0, 7) and (x ₂, y ₂) = (2, - 1) in (m ) = ( y ₂ - y ₁ ) / ( x ₂ - x ₁ ).

m = (  - 1 - 7) / (2 - 0) = - 8 / 2 = - 4.

Substitute the values of (x , y ) = (0, 7) and m = - 4 in y = mx + b.

7 = - 4(0) + b

⇒ b = 7.

Substitute the values of b = 7 and m = - 4 in y = mx + b.

y = - 4x + 7.

Therefore, the slope - intercept - form of a line equation is y = - 4x + 7.