Question

Write the equation of the line that passes through the points (4, -1)

and (3,-2).
Ox+y = -5
O y = x-5
O y = -x +3
Oy - 3x + 13

Answer 1

`y=x-5`

Explanation:

`\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=(y_2-y_1)/(x_2-x_1)$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}`

Given points:

• (x₁, y₁) = (4, -1)
• (x₂, y₂) = (3, -2)

Substitute the given points into the slope formula to find the slope of the line:

`\implies m=(-2-(-1))/(3-4)=(-1)/(-1)=1`

`\boxed{\begin{minipage}{5cm}\underline{Point-slope Formula}\\\\$y-y_1=m(x-x_1)$\\\\where $m$ is the slope and\\ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}`

Substitute the found slope and the point (4, -1) into the point-slope formula to create the equation of the line:

`\implies y-(-1)=1(x-4)`

`\implies y+1=x-4`

`\implies y+1-1=x-4-1`

`\implies y=x-5`