If, by "put it into slope-intercept form", you mean write the equation as y= mx+ b, you need to know the slope to use that! Of course, one way to answer this is to treat y= mx+ b as an equation in the two unknown values m and b. To solve for two unknowns, you need two equations- and you have those by using the two sets of values given.

"it costs $2200 to produce 100 chairs in one day" so, letting x be the number of chairs produced and letting y be the cost, x= 100, y= 2200 and the equation becomes 2200= 100m+ b.

"and $4800 to produce 300 chairs in one day." Okay, now x= 300 and y= 4800: 4800= 300m+ b.

Solve those two equations for m and b.

In fact, since the question only asks for the slope, m, use that fact that if you subtract one equation from the other, b cancels out.