# SOLUTION: Determine the algebraic rule for the line that: satisfies f(0) = -2 and f(4) = 5

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 Click here to see ALL problems on Functions Question 124962This question is from textbook Intermediate Algebra Review : Determine the algebraic rule for the line that: satisfies f(0) = -2 and f(4) = 5This question is from textbook Intermediate Algebra Review Answer by jim_thompson5910(28715)   (Show Source): You can put this solution on YOUR website!Since f(0) = -2, we have the first point (0,-2). Also, because f(4) = 5, we have the second point (4,5) So let's find the equation of the line that goes through (0,-2) and (4,5) First lets find the slope through the points (,) and (,) Start with the slope formula (note: is the first point (,) and is the second point (,)) Plug in ,,, (these are the coordinates of given points) Subtract the terms in the numerator to get . Subtract the terms in the denominator to get So the slope is ------------------------------------------------ Now let's use the point-slope formula to find the equation of the line: ------Point-Slope Formula------ where is the slope, and is one of the given points So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Rewrite as Distribute Multiply and to get . Now reduce to get Subtract from both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line which goes through the points (,) and (,) is: (note: in function notation the equation is ) The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver) Graph of through the points (,) and (,) Notice how the two points lie on the line. This graphically verifies our answer.