The graph of a linear function is shown on the grid. plotted points are Y 12,11 X -3, -4

Question

Which equation is best represented by this graph?.

Answer 1

To determine the equation of the linear function represented by the points Y(12, 11) and X(-3, -4), we first need to find the slope (m) of the line that passes through these two points.

1. Finding the slope (m): The slope is calculated using the formula: $$m=\frac{y_2-y_1}{x_2-x_1}$$ Using the points (x1, y1) = (-3, 12) and (x2, y2) = (-4, 11): $$m=\frac{11-12}{-4-(-3)}=\frac{-1}{-1}=1$$

2. Finding the y-intercept (b): We can use the slope-intercept form of the line: $$y=mx+b$$ Now we can plug in one of the points to find b. Let's use the point (-3, 12): $$12=1(-3)+b$$ $$12=-3+b$$ $$b=12+3=15$$

3. Writing the equation: Now that we have the slope (m = 1) and the y-intercept (b = 15), we can write the equation of the line: $$y=1x+15$$ or simply $$y=x+15$$

Thus, the equation best represented by the graph is:

$$y=x+15$$

Answer 2

wrong

Answer 3

I apologize for the oversight. Let’s correctly find the equation of the linear function using the provided points more carefully.

You mentioned the points $(Y,12,11)$ and $(X,-3,-4)$, which seem to indicate two separate points on the graph. Let's clarify the points as follows:

1. Identify the Points:

   • Let’s assume the points are $(-3,12)$ and $(-4,11)$.

2. Calculate the Slope (m): The slope $m$ is calculated with the formula: $$m=\frac{y_2-y_1}{x_2-x_1}$$ For points $(-3,12)$ and $(-4,11)$: $$(x_1,y_1)=(-3,12)\text{and}(x_2,y_2)=(-4,11)$$ $$m=\frac{11-12}{-4-(-3)}=\frac{-1}{-4+3}=\frac{-1}{-1}=1$$

3. Finding the y-intercept (b): Now we use the slope-intercept form of the line $y=mx+b$. Plug in the slope and one of the points to solve for $b$. Let’s use the point $(-3,12)$: $$12=1(-3)+b$$ $$12=-3+b$$ $$b=12+3=15$$

4. Equation of the Line: Thus, the equation based on the points should be: $$y=1x+15\text{or}y=x+15$$ However, since you're indicating that the initial calculation is wrong, let’s carefully verify if I misunderstood the points.

Let's Re-evaluate the Points:

If the points were $(x_1,y_1)=(-3,12)$ and $(x_2,y_2)=(-4,11)$:

• The y-coordinates reflect vertical points.
• The slope is calculated based on the definition: $\text{slope}=\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}$
• Ensure that they are consistent in the explanation of points.

If you have specific corrections on how I interpreted those points or need new points to clarify, please provide them so I can assist you correctly. Thank you!