which of the following is the equation that corresponds to the graph depicted below? f(x)=2x - 3 g(x)=-2x +…

which of the following is the equation that corresponds to the graph depicted below? f(x)=2x - 3 g(x)=-2x + 3 h(x)=-2x - 3 k(x)=2x + 3 m(x)=\\frac{1}{2}x + 3 n(x)=-\\frac{1}{2}x + 3 p(x)=\\frac{1}{2}x - 3 q(x)=-\\frac{1}{2}x - 3

which of the following is the equation that corresponds to the graph depicted below? f(x)=2x - 3 g(x)=-2x + 3 h(x)=-2x - 3 k(x)=2x + 3 m(x)=\\frac{1}{2}x + 3 n(x)=-\\frac{1}{2}x + 3 p(x)=\\frac{1}{2}x - 3 q(x)=-\\frac{1}{2}x - 3

Answer

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Determine the slope

The line is increasing, so the slope $m>0$. Also, for every 1 unit increase in $x$, $y$ increases by 2 units. So $m = 2$.

Step3: Determine the y - intercept

The line crosses the y - axis at the point $(0,- 3)$, so $b=-3$.

Step4: Identify the equation

The equation of the line is $y = 2x-3$, which is $f(x)=2x - 3$.

Answer:

$f(x)=2x - 3$