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GED Math : Graphing Lines

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Example Question #1 : Graphing Lines

A line has slope $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ and $\displaystyle y$-intercept (0, -7) $\displaystyle (0, -7)$. Give its $\displaystyle x$-intercept.

Possible Answers:

$\left (- 9 \frac{1}{3}, 0 \right )$ $\displaystyle \left (- 9 \frac{1}{3}, 0 \right )$

$\left (-5\frac{1}{4}, 0 \right )$ $\displaystyle \left (-5\frac{1}{4}, 0 \right )$

$\left (5\frac{1}{4}, 0 \right )$ $\displaystyle \left (5\frac{1}{4}, 0 \right )$

$\left ( 9 \frac{1}{3}, 0 \right )$ $\displaystyle \left ( 9 \frac{1}{3}, 0 \right )$

Correct answer:

$\left ( 9 \frac{1}{3}, 0 \right )$ $\displaystyle \left ( 9 \frac{1}{3}, 0 \right )$

Explanation:

The $\displaystyle x$-intercept will be a point (a,0) $\displaystyle (a,0)$ for some value $\displaystyle a$. We use the slope formula

$\frac{y_{2}- y _{1}}{x_{2}- x _{1}} = m$ $\displaystyle \frac{y_{2}- y _{1}}{x_{2}- x _{1}} = m$,

setting $m = \frac{3}{4}, x_{1} =0, x_{2} = a, y_{1} = -7, y_{2} =0$ $\displaystyle m = \frac{3}{4}, x_{1} =0, x_{2} = a, y_{1} = -7, y_{2} =0$,

and solving for $\displaystyle a$:

$\frac{0- (-7)}{a-0} = \frac{3}{4}$ $\displaystyle \frac{0- (-7)}{a-0} = \frac{3}{4}$

$\frac{ 7}{a} = \frac{3}{4}$ $\displaystyle \frac{ 7}{a} = \frac{3}{4}$

$\frac{ 7}{a} \cdot a = \frac{3}{4} \cdot a$ $\displaystyle \frac{ 7}{a} \cdot a = \frac{3}{4} \cdot a$

$7= \frac{3}{4} \cdot a$ $\displaystyle 7= \frac{3}{4} \cdot a$

$\frac{4} {3}\cdot 7= \frac{4} {3}\cdot \frac{3}{4} \cdot a$ $\displaystyle \frac{4} {3}\cdot 7= \frac{4} {3}\cdot \frac{3}{4} \cdot a$

$a = \frac{28} {3} = 9 \frac{1}{3}$ $\displaystyle a = \frac{28} {3} = 9 \frac{1}{3}$

The $\displaystyle x$-intercept is $\left ( 9 \frac{1}{3}, 0 \right )$ $\displaystyle \left ( 9 \frac{1}{3}, 0 \right )$.

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Example Question #1 : Graphing Lines

A line has slope $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ and $\displaystyle x$-intercept (5, 0) $\displaystyle (5, 0)$. Give its $\displaystyle y$-intercept.

Possible Answers:

$\left (0, 3 \frac{3}{4} \right )$ $\displaystyle \left (0, 3 \frac{3}{4} \right )$

$\left (0, -3 \frac{3}{4} \right )$ $\displaystyle \left (0, -3 \frac{3}{4} \right )$

$\left (0, 6 \frac{2} {3}\right )$ $\displaystyle \left (0, 6 \frac{2} {3}\right )$

$\left (0, -6 \frac{2} {3}\right )$ $\displaystyle \left (0, -6 \frac{2} {3}\right )$

Correct answer:

$\left (0, -3 \frac{3}{4} \right )$ $\displaystyle \left (0, -3 \frac{3}{4} \right )$

Explanation:

The $\displaystyle y$-intercept will be the point (0, b) $\displaystyle (0, b)$ for some value $\displaystyle b$. We use the slope formula

$\frac{y_{2}- y _{1}}{x_{2}- x _{1}} = m$ $\displaystyle \frac{y_{2}- y _{1}}{x_{2}- x _{1}} = m$,

setting $m = \frac{3}{4}, x_{1} = 5, x_{2} = 0, y_{1} = 0, y_{2} = b$ $\displaystyle m = \frac{3}{4}, x_{1} = 5, x_{2} = 0, y_{1} = 0, y_{2} = b$,

and solving for $\displaystyle b$:

$\frac{b-0}{0- 5} = \frac{3}{4}$ $\displaystyle \frac{b-0}{0- 5} = \frac{3}{4}$

$\frac{b }{ - 5} = \frac{3}{4}$ $\displaystyle \frac{b }{ - 5} = \frac{3}{4}$

$\frac{b }{ - 5} \cdot (-5) = \frac{3}{4} \cdot (-5)$ $\displaystyle \frac{b }{ - 5} \cdot (-5) = \frac{3}{4} \cdot (-5)$

$b= \frac{-15}{4} = -3 \frac{3}{4}$ $\displaystyle b= \frac{-15}{4} = -3 \frac{3}{4}$

The $\displaystyle y$-intercept is $\left (0, -3 \frac{3}{4} \right )$ $\displaystyle \left (0, -3 \frac{3}{4} \right )$.

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GED Math : Graphing Lines

Study concepts, example questions & explanations for GED Math

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Example Question #1 : Graphing Lines

Example Question #1 : Graphing Lines

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