Graphing Lines

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1

A line has slope $\frac{3}{4}$ and -intercept . Give its -intercept.

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

CORRECT

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

0

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

0

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

0

Explanation

The -intercept will be a point for some value . We use the slope formula

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

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

and solving for :

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

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

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

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

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

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

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

2

A line has slope $\frac{3}{4}$ and -intercept . Give its -intercept.

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

CORRECT

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

0

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

0

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

0

Explanation

The -intercept will be the point for some value . We use the slope formula

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

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

and solving for :

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

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

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

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

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

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