Finding y intercept given slope & point (old)
About this video
Sal finds the y-intercept b of the line y = (17/13)x + b that passes through (5, 8). He substitutes the point, simplifies to 8 = 85/13 + b, and rewrites 8 as 104/13 to get b = 19/13.
You'll be able to
- substitute a point into a line's equation to find b.
- multiply a fraction by a whole number.
- subtract fractions by rewriting a whole number with a common denominator.
Key words
- y-intercept
- The value b in y = mx + b; where the line crosses the y-axis.
- satisfy an equation
- A point satisfies an equation if putting its x and y values in makes the equation true.
Transcript
The following line passes through the point 5 comma 8, and the equation of the line is y is equal to 17/13x 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 that when x is equal to 5, y is equal to 8.
So we can say-- so when x is equal to 5, y is equal to 8. So we can say 8 must be equal to 17/13 times x times 5 plus b, and then we can solve for b. So if we simplify this a little bit, we get 8 is equal to-- let's see, 5 times 17 is 50, plus 35 is 85-- is 85/13 plus b.
Then to solve for b, we just subtract 85/13 from both sides. So we have 8 minus 85/13. 85/13 Is equal to b. And now we just have to subtract these two numbers. So 8 is the same thing as-- let's see. 80 plus 24 is 104, so it is 104/13-- this is the same thing as 8-- minus 85/13, which is going to be-- let's see.
This is 19/13. Is that right? Yes, if this was 105, then it would be 20/13. So this is 19/13, so it's equal to 19/13, which is equal to b. So the equation of this line is going to be y is equal to 17/13x plus 19/13.
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