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the following line passes through the point 5 comma 8 and the line the equation of line is y is equal to 17 thirds 1713 X plus B what is the value of the y-intercept B so we know that this point this x and y value must satisfy this equation so we know we know that when X is equal to 5 y is equal to 8 so we can say we can say so when X is equal to 5 y is equal to Y is equal to 8 so we could say 8 must be equal to 17 over 13 times X times 5 plus B and that we can solve for B so this if we simplify this a little bit we get 8 is equal to C 5 times 17 is 50 plus 35 is 85 is 85 over 13 plus B then to solve for B we just subtract 85 over 13 from both sides so we have 8/8 minus 85 over 13 85 over 13 is equal to B and now we just have to add these two or subtract these two numbers so 8 is the same thing as let's see 80 plus 24 is 104 so it is 104 over 13 this is the same thing as 8 minus 85 over 13 which is going to be let's see this is 19 over 13 is that right yes this is 105 the node would be 20 over 13 this is 19 over 13 so it's equal to 19 over 13 which is equal to B so the equation of this line is going to be y is equal to 17 13 X plus 19 over 13