Write an equation in slope-intercept form for each table below. Show how you found the slope and y-intercept.

Table (1):

| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y | 0 | 2.5 | 5 | 7.5 | 10 |

Steps to find the slope (m) and y-intercept (b):

1. Calculate the slope (m) using two points from the table:
\( m = \frac{y_2 - y_1}{x_2 - x_1} \)

Let's use the points (0, 0) and (1, 2.5):
\( m = \frac{2.5 - 0}{1 - 0} = 2.5 \)

2. Determine the y-intercept (b) by identifying the y-value when x = 0:
The y-intercept is 0.

Equation in slope-intercept form:
\[ y = 2.5x + 0 \]
Or simply:
\[ y = 2.5x \]

x=1;\ y=2.5\\x=2;\ y= 5\\\\The\ slope-intercept\ form:y=mx+b\\\\subtitute:\\\\ - \left\{\begin{array}{ccc}2.5=1m+b\\5=2m+b\end{array}\right\ \ \ |subtract\ both\ sides\ of\ equations\\--------\\.\ \ \ \ -2.5=-m\\.\ \ \ \ \ m=2.5\\\\subtitute\ value\ of\ m\ to\ the\ equation\ 2.5=1m+b\\\\2.5=2.5+b\\2.5+b=2.5\ \ \ \ |subtract\ 2.5\ from\ both\ sides\\b=0\\\\Therefore,\ answer\ is:\boxed{y=2.5x+0=2.5x}
C h ec k : x = 0 ; y = 0 0 = 2.5 ⋅ 0 0 = 0 − correc t x = 3 ; y = 7.5 7.5 = 2.5 ⋅ 3 7.5 = 7.5 − correc t x = 4 ; y = 10 10 = 2.5 ⋅ 4 10 = 10 − correc t

Answered by Anonymous | 2024-06-10

The equation in slope-intercept form for the given table is y = 2.5 x . We calculated the slope as 2.5 and the y-intercept as 0. The equation correctly describes the relationship between x and y in the provided data.
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Answered by Anonymous | 2025-04-11