Answer:
[tex]y=-4x+1[/tex]
Step-by-step explanation:
We have been given two points on the line, so:
[tex]\textsf{let}\:(x_1,y_1)=(-1,5)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(1,-3)[/tex]
Calculate the slope using the slope formula:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-3-5}{1-(-1)}=-4[/tex]
From inspection of the graph, it appears that the y-intercept (where the line crosses the y-axis) is at (0, 1). However, just to be sure, use the point-slope form of linear equation.
Point-slope form of linear equation: [tex]y-y_1=m(x-x_1)[/tex]
(where m is the slope and (x₁, y₁) is a point on the line)
[tex]\implies y-5=-4(x-(-1))[/tex]
[tex]\implies y-5=-4x-4[/tex]
[tex]\implies y=-4x+1[/tex]
Therefore, the equation of the line in slope-intercept form is:
[tex]y=-4+1[/tex]
