Question

find the equation of the linear function represented by the table below in slope-intercept form.
x | y
1 | 9
2 | 14
3 | 19
4 | 24

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using points (1, 9) and (2, 14):
$m = \frac{14 - 9}{2 - 1} = \frac{5}{1} = 5$.

Step2: Find the y-intercept (b)

Slope-intercept form is $y = mx + b$. Substitute $m = 5$ and a point (e.g., (1, 9)):
$9 = 5(1) + b$
$9 = 5 + b$
$b = 9 - 5 = 4$.

Step3: Write the equation

Substitute $m = 5$ and $b = 4$ into $y = mx + b$:
$y = 5x + 4$.

Answer:

$y = 5x + 4$