Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 2 - Functions, Equations, and Graphs - 2-4 More About Linear Equations - Lesson Check: 2

Answer

$y=\frac{1}{2}x+2$

Work Step by Step

RECALL: The slope-intercept form of a line's equation is $y=mx + b$, where m=slope and b=y-intercept. The line has a slope of $\frac{1}{2}$, so $m=\frac{1}{2}$. This means that the tentative equation of the line is $y=\frac{1}{2}x+b$. The line passes through the point (2, 3), which means that the coordinates of this point satisfies the equation of the line. Substitute the x and y coordinates of the given point into the tentative equation above to have $y=\frac{1}{2}x+b \\3 = \frac{1}{2}(2) + b \\3 =1 + b \\3-1 = b \\2=b.$ Thus, the equation of the line is $y=\frac{1}{2}x+2$.
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