Question

find the equation of the linear function represented by the table below in slope - intercept form

x	0	1	2	3	4
y	5	12	19	26	33

Explanation:

Step1: Find the slope (m)

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the first two points \((0, 5)\) and \((1, 12)\):
\( m=\frac{12 - 5}{1 - 0}=\frac{7}{1} = 7 \)

Step2: Find the y-intercept (b)

The slope - intercept form of a line is \( y=mx + b \). When \( x = 0 \), \( y=b \). From the table, when \( x = 0 \), \( y = 5 \), so \( b = 5 \).

Step3: Write the equation

Substitute \( m = 7 \) and \( b = 5 \) into the slope - intercept form \( y=mx + b \):
\( y=7x + 5 \)

Answer:

\( y = 7x+5 \)