Question

Which equation represents the graphed function?

Answer 1

Solution:

we have been asked to find

Which equation represents the graphed function?

As we can see in the graph, the line is passing through the point (2,0) and (0,-3).

As we know the equation of the passing through two points is given by the formula

$(y-y_1)=m(x-x_1)\\ \\ m=slope=\frac{y_2-y_1}{x_2-x_1}=\frac{-3-0}{0-2}=\frac{3}{2}$

So the equation of the line will be

$y-0=\frac{3}{2}(x-2)\\ \\ y= \frac{3}{2}x-3$

Answer 2

The equation which represents the graphed function is $\fbox{\begin\\\ \math y=\dfrac{3x}{2}-3\\\end{minispace}}$.

Further explanation:

From the given graph of a function it is observed that the curve intersects the $x$-axis at one point and intersects the $y$-axis at one point.

This implies that there is one $x$-intercept and one $y$-intercept.

$x$-intercept is defined as a point where the curve intersects the $x$-axis.

$y$-intercept is defined as a point where the curve intersects the $y$-axis.

From the given graph it is observed that the point where the curve intersects the $x$-axis is $(2,0)$ and the point where the curve intersects the $y$-axis is $(0,-3)$.

Therefore, the line passes through the points $(2,0)$ and $(0,-3)$.

Slope of a curve is defined as the change in the value of $y$ with respect to change in value of $x$.

The slope of the line is calculated as follows:

$\fbox{\begin\\\ \math m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\end{minispace}}$

The point $(x_{1},y_{1})$ and $(x_{2},y_{2})$ for the given line are $(2,0)$ and $(0,-3)$.

The value of slope of the given line is calculated as follows:

$\begin{aligned}m&=\dfrac{-3-0}{0-2}\\&=\dfrac{-3}{-2}\\&=\dfrac{3}{2}\end{aligned}$

Therefore, the slope of the line is $\fbox{\begin\\\ \math m=\dfrac{3}{2}\\\end{minispace}}$.

The slope intercept form of a line is as follows:

$\fbox{\begin\\\ \math y=mx+c\\\end{minispace}}$      (1)

In the above equation $m$ represents the slope and $c$ represents the $y$-intercept.

From the graph it is observed that the value of $c$ is $-3$.

To obtain the equation of the line substitute $-3$ for $c$ and $\dfrac{3}{2}$ for $m$ in equation (1).

$y=\dfrac{3}{2}x-3$

Therefore, the equation which represents the line in the given graph is $\fbox{\begin\\\ \math y=\dfrac{3}{2}x-3\\\end{minispace}}$.

Learn more:

1. A problem to complete the square of quadratic function brainly.com/question/12992613  

2. A problem to determine the slope intercept form of a line brainly.com/question/1473992

3. Inverse function brainly.com/question/1632445  

Answer details

Grade: High school

Subject: Mathematics  

Chapter: Linear equation

Keywords: Equation, linear equation, slope, intercept, x-intercept, y-intercept, intersect, graph, curve, slope intercept form, line, y=3x/2-3, (2,0), (0,-3), point slope form.