Question

slope-intercept form - item 35340
complete the slope-intercept form of the linear equation that represents the relationship in the table.

x	y
3	-5
-2	5

y = \square x + \square

Explanation:

Step1: Calculate the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points (3, -5) and (-2, 5), we have $x_1 = 3$, $y_1 = -5$, $x_2 = -2$, $y_2 = 5$.
So, $m = \frac{5 - (-5)}{-2 - 3} = \frac{10}{-5} = -2$.

Step2: Find the y-intercept (b)

Use the slope-intercept form $y = mx + b$ and one of the points, say (3, -5). Substitute $m = -2$, $x = 3$, and $y = -5$ into the equation:
$-5 = -2(3) + b$
$-5 = -6 + b$
Add 6 to both sides: $b = -5 + 6 = 1$.

Answer:

$y = -2x + 1$