Question

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

Answer 1

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

» Finding the slope [m] :

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

• 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:

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

» Finding y-intercept [c] :

☑ REMEMBER: y = mx + c

• Consider point (0, -2)

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

» Arrange the equation:

Equation is y = ⅔x - 2