Respuesta :
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.
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 ⤵️
[tex] \boxed{ \sf \:m = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1}} }[/tex]
- (x1,y1) = (-4,-5)
- (x2,y2) = (-8,-2)
[tex] \tt \to \: m = \frac{ - 2-( - 5)}{ - 8 -(- 4)} [/tex]
[tex] \tt \to \: m = \frac{ -2+5}{ -8+4} [/tex]
[tex] \tt \to \: m = - \frac{3}{4} [/tex]
Now, Put the values in the formula used to find the equation ⤵️
[tex] \boxed{ \sf \:y - y_{1} = m(x - x_{1}) }[/tex]
- (x1,y1) = (-4,-5)
[tex] \tt \nrightarrow \: y - ( - 5) = - \frac{3}{4} (x - ( - 4))[/tex]
[tex] \tt \nrightarrow \: y + 5 = - \frac{3}{4} (x + 4)[/tex]
[tex] \tt \nrightarrow \: y + 5 = - \frac{3}{4} x - 3[/tex]
[tex] \tt \nrightarrow \: y = - \frac{3}{4} x - 3 - 5[/tex]
[tex] \bf\nrightarrow \: y = - \frac{3}{4} x - 8[/tex]
