Question

What is an equation of the line that passes through the points (-4, -5) and (-8, -2)?

Answer 1

Solution:

Step-1: Find the slope of the line.

Formula of slope: y₂ - y₁/x₂ - x₁

• y₂ - y₁/x₂ - x₁ = Slope
• => -2 - (-5)/-8 - (-4) = Slope
• => -2 + 5/-8 + 4 = Slope
• => 3/-4 = Slope

Step-2: Use the point slope formula to determine the slope.

Point slope form formula: y - y₁ = m(x - x₁)

• y - y₁ = m(x - x₁) = Equation of line
• => y - (-5) = -3/4{x - (-4)} = Equation of line
• => y + 5 = -3/4{x + 4} = Equation of line
• => y + 5 = -3x/4 - 3 = Equation of line
• => y = -3x/4 - 8 = Equation of line

The equation of the line is y = -3x/4 - 8.

Answer 2

To find the equation, First step is to find the slope which we can use in the formula and then we will find the equation using the specific formula...

Finding slope ⤵️

$\boxed{ \sf \:m = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1}} }$

• (x1,y1) = (-4,-5)
• (x2,y2) = (-8,-2)

$\tt \to \: m = \frac{ - 2-( - 5)}{ - 8 -(- 4)}$

$\tt \to \: m = \frac{ -2+5}{ -8+4}$

$\tt \to \: m = - \frac{3}{4}$

Now, Put the values in the formula used to find the equation ⤵️

$\boxed{ \sf \:y - y_{1} = m(x - x_{1}) }$

• (x1,y1) = (-4,-5)

$\tt \nrightarrow \: y - ( - 5) = - \frac{3}{4} (x - ( - 4))$

$\tt \nrightarrow \: y + 5 = - \frac{3}{4} (x + 4)$

$\tt \nrightarrow \: y + 5 = - \frac{3}{4} x - 3$

$\tt \nrightarrow \: y = - \frac{3}{4} x - 3 - 5$

$\bf\nrightarrow \: y = - \frac{3}{4} x - 8$