Question

1 fill in the blank 1 point a linear relationship includes the ordered pairs (4, 9) and (10, 21). write an equation in slope - intercept form that can be used to model the relationship. options: 1, 1.5, 2, 2.5, 3 y = type your answer... x + type your answer...

Explanation:

Step1: Calculate the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Using \((4, 9)\) as \((x_1, y_1)\) and \((10, 21)\) as \((x_2, y_2)\):
\(m = \frac{21 - 9}{10 - 4} = \frac{12}{6} = 2\)

Step2: Find the y-intercept (b)

Use the slope-intercept form \(y = mx + b\) and one of the points, say \((4, 9)\), and \(m = 2\):
\(9 = 2(4) + b\)
\(9 = 8 + b\)
Subtract 8 from both sides: \(b = 9 - 8 = 1\)

Answer:

\(y = 2x + 1\)