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AysviL [449]
2 years ago
11

This graph represents a linear function. Which equation is represented by this graph?

Mathematics
1 answer:
lisabon 2012 [21]2 years ago
3 0

Answer:

Answer is A

Step-by-step explanation:

» Consider two points plotted on the line;

  • (3, 0) and (0, -2)

» General equation of a line has an expression in format of;

{ \rm{y = mx + c}}

  • m is the slope
  • c is the y-intercept

<u>»</u><u> </u><u>F</u><u>i</u><u>n</u><u>d</u><u>i</u><u>n</u><u>g</u><u> </u><u>t</u><u>h</u><u>e</u><u> </u><u>s</u><u>l</u><u>o</u><u>p</u><u>e</u><u> </u><u>[</u><u>m</u><u>]</u><u> </u><u>:</u>

{ \rm{slope =  \frac{y_{2}  - y _{1}}{x _{2}  - x _{1} } }} \\

• But remember from the points or coordinates we fetched out of the graph;

  • { \tt{y_{2} =  - 2}} \:  \mid \: { \tt{y_{1} = 0}} \\ { \tt{x_{2} =0 }} \:   \mid \:  { \tt{x_{1} = 3}}

Therefore, lets feed in the formular:

{ \tt{m =  \frac{ {}^{ - } 2 - 0}{0 - 3} =  \frac{ - 2}{ - 3}  }} \\  \\ { \boxed{ \tt{m =  \frac{2}{3} }}}

<u>»</u><u> </u><u>F</u><u>i</u><u>n</u><u>d</u><u>i</u><u>n</u><u>g</u><u> </u><u>y</u><u>-</u><u>i</u><u>n</u><u>t</u><u>e</u><u>r</u><u>c</u><u>e</u><u>p</u><u>t</u><u> </u><u>[</u><u>c</u><u>]</u><u> </u><u>:</u>

☑ <em>R</em><em>E</em><em>M</em><em>E</em><em>M</em><em>B</em><em>E</em><em>R</em><em>:</em><em> </em>y = mx + c

• Consider point (0, -2)

{ \tt{y = mx + c}} \\ { \tt{ - 2 = ( \frac{2}{3}  \times 0) + c}} \\ \\  { \boxed{ \tt{ \: c =  - 2 \: }}}

<u>»</u><u> </u><u>A</u><u>r</u><u>r</u><u>a</u><u>n</u><u>g</u><u>e</u><u> </u><u>t</u><u>h</u><u>e</u><u> </u><u>e</u><u>q</u><u>u</u><u>a</u><u>t</u><u>i</u><u>o</u><u>n</u><u>:</u>

Equation is y = ⅔x - 2

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