The equation of the graphed line passing through the points (-1,4) and (1,-2) is y = -3x + 1.
The equation of a line in slope-intercept form is expressed as:
y = mx + b
From the graph, the line passes through the points (-1,4) and (1,-2).
First, we determine the slope:
Slope m = ( change in y ) / ( change in x )
Slope m = ( -2 - 4 ) / ( 1 - (-1) )
Slope m = -6/2
Slope = -3
Now, plug the slope m = -6 and point (1,-2) into the point-slope formula and simplify:
y - y₁ = m( x - x₁ )
y - (-2) = -3( x - 1 )
y + 2 = -3x + 3
y + 2 - 2 = -3x + 3 - 2
y = -3x + 1
Therefore, the equation of the line is y = -3x + 1.