Write an equation from slope-intercept form (

Question

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y=mx+b ) from the table below. Click Here for Help Video.

𝑥
x
𝑦
y
9
9
−
12
−12
18
18
−
19
−19
27
27
−
26
−26


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Answer 1

To find the equation in slope-intercept form $y=mx+b$ from the given table, we first need to determine the slope $m$ and the y-intercept $b$.

Here are the data points from the table:

• (9, 9)
• (18, -19)
• (27, -26)

Step 1: Calculate the slope $m$

The slope formula is given by: $$m=\frac{y_2-y_1}{x_2-x_1}$$

Using the first two points (9, 9) and (18, -19):

• $x_1=9$
• $y_1=9$
• $x_2=18$
• $y_2=-19$

Now, we can substitute in the values: $$m=\frac{-19-9}{18-9}=\frac{-28}{9}=-\frac{28}{9}$$

Next, let's use the second and third points (18, -19) and (27, -26):

• $x_1=18$
• $y_1=-19$
• $x_2=27$
• $y_2=-26$

Substituting those values: $$m=\frac{-26-(-19)}{27-18}=\frac{-26+19}{9}=\frac{-7}{9}$$

Now we need to ensure we have consistent slopes. Using the first point and any of the derived points will give us the same slope due to being linear.

Step 2: Find the y-intercept $b$

We can use one of the points and the slope to find $b$. Let's use the point (9, 9).

Substitute into the equation $y=mx+b$: $$9=-\frac{28}{9}(9)+b$$

Calculating it: $$9=-28+b$$ $$b=9+28=37$$

Final Equation

Now we have $m=-\frac{28}{9}$ and $b=37$.

Thus, the equation in slope-intercept form is: $$y=-\frac{28}{9}x+37$$

If preferred, we can also express it as: $$y=-\frac{28}{9}x+37$$