Question

a linear relationship includes the ordered pairs (2, 5) and (6, 13).
write a linear equation in slope - intercept form that models the relationship.
move the correct answer to each box. not all answers will be used.
y = \boxed{}x + \boxed{}
drag & drop the answer
1.5 -1 2 -2 1
note: use ctrl+d to drag the option via keyboard

Explanation:

Step1: Calculate the slope

The formula for slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using \((2, 5)\) and \((6, 13)\), we have \( m=\frac{13 - 5}{6 - 2}=\frac{8}{4} = 2 \).

Step2: Find the y - intercept

Slope - intercept form is \( y=mx + b \). We know \( m = 2 \) and we can use the point \((2, 5)\). Substitute \( x = 2 \), \( y = 5 \) and \( m = 2 \) into the equation: \( 5=2\times2 + b \). Simplify: \( 5 = 4 + b \). Subtract 4 from both sides: \( b=5 - 4=1 \).

Answer:

\( y = \boldsymbol{2}x+\boldsymbol{1} \)