[tex]y=-\frac{4}{9}x-\frac{7}{9}[/tex]
EXPLANATION
Given two points of a line, we can find the the equation of that line using the steps below:
• Step 1
Determine the slope of the line, using the formula below:
[tex]\text{slope(m)}=\frac{y_2-y_1}{x_2-x_1}[/tex]
The points given are (-4, 1) and (5, -3). This implies that the coordinates are
x₁= -4 y₁=1 x₂=5 y₂=-3
Substitute the values into the formula and simplify.
[tex]m=\frac{-3-1}{5+4}=-\frac{4}{9}[/tex]
• Step 2
Determine the y-intercept(b) of the line.
Substitute x₁= -4 y₁=1 and m=-4/9 into y=mx + b and solve for intercept(b).
1 = (-4/9)(-4) + b
[tex]1=\frac{16}{9}+b[/tex]
Subtract 16/9 from both-side of the equation.
[tex]b=1-\frac{16}{9}[/tex]
[tex]b=\frac{9-16}{9}=-\frac{7}{9}[/tex]
The intercept (b) = -7/9
• Step 3
Form the equation by substituting the value of the slope and intercept into y=mx + b.
Hence, the equation of the line is:
[tex]y=-\frac{4}{9}x-\frac{7}{9}[/tex]
