Question

question 1-2
the table shown represents a linear relationship.

x	y
-8	5
0	7
12	10

drag the values below to create an equation that represents the linear relationship in the table.
\\(\frac{1}{4}\\) 7 0 3 12 -8 -7 4 \\(-\frac{1}{4}\\) -3 -4 10
\\(y = \square x + \square\\)

Explanation:

Step1: Find the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's use the points \((-8, 5)\) and \((0, 7)\).
\(m=\frac{7 - 5}{0 - (-8)}=\frac{2}{8}=\frac{1}{4}\)

Step2: Find the y-intercept (b)

The equation of a line is \(y = mx + b\). We know when \(x = 0\), \(y = 7\) (from the point \((0, 7)\)). Substituting \(x = 0\), \(y = 7\), and \(m=\frac{1}{4}\) into the equation:
\(7=\frac{1}{4}(0)+b\), so \(b = 7\)

Answer:

\(y=\frac{1}{4}x + 7\) (So the first box is \(\frac{1}{4}\) and the second box is \(7\))