Studdy AI Logo
Math  /  Algebra

Question效 A , Write the linear equation that gives the rule for this table. \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline 3 & -24 \\ \hline 4 & -32 \\ \hline 5 & -40 \\ \hline 6 & -48 \\ \hline \end{tabular} with y first, followed by an equals sign. □\square

Studdy Solution

STEP 1

1. The table represents a linear relationship between x x and y y .
2. The goal is to find the linear equation in the form y=mx+b y = mx + b .
3. The values of x x and y y are given in pairs, and we need to determine the slope m m and the y-intercept b b .

STEP 2

1. Determine the slope m m of the linear equation.
2. Use one of the points to solve for the y-intercept b b .
3. Write the linear equation in the form y=mx+b y = mx + b .

STEP 3

To find the slope m m , use the formula:
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Choose two points from the table, for example, (3,−24) (3, -24) and (4,−32) (4, -32) .

STEP 4

Substitute the chosen points into the slope formula:
m=−32−(−24)4−3=−32+241=−81=−8 m = \frac{-32 - (-24)}{4 - 3} = \frac{-32 + 24}{1} = \frac{-8}{1} = -8
The slope m m is −8 -8 .

STEP 5

Use the slope m=−8 m = -8 and one of the points, say (3,−24) (3, -24) , to find the y-intercept b b .
Substitute into the equation y=mx+b y = mx + b :
−24=−8(3)+b -24 = -8(3) + b

STEP 6

Solve for b b :
−24=−24+b -24 = -24 + b
b=0 b = 0
The y-intercept b b is 0 0 .

STEP 7

Write the linear equation using the slope m=−8 m = -8 and the y-intercept b=0 b = 0 :
y=−8x+0 y = -8x + 0
Simplify the equation:
y=−8x y = -8x

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord