Mathematics, 02.07.2019 09:40 jeremymcdonaldorlh0s

Which equation represents the graphed function? a. –3x + 2 = y b. –x + 2 = y c. x – 3 = y d. 2x – 3 = y

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Answer from: PrincessAlaia01

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 from: arivalen

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 -axis at one point and intersects the -axis at one point.

This implies that there is one -intercept and one -intercept.

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

From the given graph it is observed that the point where the curve intersects the -axis is (2,0) and the point where the curve intersects the -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 with respect to change in value of .

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 represents the slope and represents the -intercept.

From the graph it is observed that the value of is .

To obtain the equation of the line substitute for and $\dfrac{3}{2}$ for 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 link

2.A problem to determine the slope intercept form of a line link

3.Inverse function link

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.

Answer from: Quest

Idon’t understand this but 90

Answer from: Quest

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Which equation represents the graphed function? a. –3x + 2 = y b. –x + 2 = y c. x – 3 = y d. 2x –...

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