The equation for the linear function whose graph passes through the points (-1, -2) and (3, 10) in point-slope form is y + 2 = 3( x + 1 ).
The point-slope form of a line is expressed as;
( y - y₁ ) = m( x - x₁ )
Given that, the line contains the points (-1, -2) and (3, 10).
First, we determine the slope m.
Slope m = ( change in y ) / ( change in x )
Slope m = ( 10 - (-2) ) / ( 3 - (-1) )
Slope m = ( 10 + 2 ) / ( 3 + 1 )
Slope m = 12/4
Slope = 3
Plug the slope m = 3 and point (-1, -2) into the point-slope formula and simplify.
( y - y₁ ) = m( x - x₁ )
y - (-2) = 3( x - (-1) )
Simplifying, we get:
y + 2 = 3( x + 1 )
Therefore, the equation of the graph in point-slope form is y + 2 = 3( x + 1 ).