## Algebra 1

Published by Prentice Hall

# Chapter 6 - Systems of Equations and Inequalities - 6-1 Solving Systems by Graphing - Practice and Problem-Solving Exercises - Page 363: 11

#### Answer

The point of intersection is $(4,9)$

#### Work Step by Step

#$1$ The standard notation for linear functions is $y=mx + b$, where $m=slope$ of the function (rise over run) and $b=$ the y-intercept of the function. #$2$ For Equation 1,$y = \frac{1}{2}x+7$ , the $m$ value is $\frac{1}{2}$, which means the slope is $\frac{1}{2}$ in other words this means for every increase of $2$ in the positive x- direction the y-value will increase by $1$ in the positive y-direction. There is $b$ value of $7$so the y-intercept is $(0,7)$. $y = \frac{1}{2}x+7;slope= \frac{1}{2} and y−intercept=(0,7)$ #$3$ Equation 2, $y=\frac{3}{2}x+3$, the $m$ value, or slope, is $\frac{3}{2}$, which means for every increase of $2$ in the positive x-direction the y- value will increase by $3$ There is $b$ value so the y-intercept is $(0,3)$ $y=\frac{3}{2}x+3 ;slope=\frac{3}{2} and y−intercept=(0,3)$ #$4$ When we graph the $2$ functions, Equation $1$ corresponds with $f(x)=\frac{1}{2}x+7$ in the $blue color$ and we can see that it has a slope of $\frac{1}{2}$ and its y-intercept is at $(0,7)$. Equation $2$ corresponds with $g(x)=\frac{3}{2}x+3$ in the $red color$ and it has a slope of $\frac{3}{2}$ and its y-intercept is at $(0,3)$. We can see in the graph that the two functions intersect at $(4,9)$. This means that the two functions equal one another at this point. #$5$ We can double check our result by making the functions equal one another and solving for $x$. After doing this we find that the two functions equal one another when $x=4$. By plugging this back into the functions we can check this again because when $x=4$ both functions are $y=9$. Solution- $\frac{1}{2}x+7 = \frac{3}{2}x+3$ ........$-3 . . . . . . .-3$ $\frac{1}{2}x + 4 = \frac{3}{2}x$ $0.5x + 4 = 1.5x$ $-0.5x . . . . -0.5x$ $4 = 1x$ $x = 4$

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