Question

1.
x | 0 | 5 | 10 | 15
y | -2 | 40.5 | 83 | 125.5
m: ____ b: ____
equation: y=
apply your knowledge of slope - intercept form to ans

1. mia has $50 on a gift card to her favorite

4.

Explanation:

Step1: Calculate the slope (m)

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take the points \((0, - 2)\) and \((5,40.5)\).
\( m=\frac{40.5-(-2)}{5 - 0}=\frac{40.5 + 2}{5}=\frac{42.5}{5}=8.5=\frac{17}{2}\)

Step2: Determine the y - intercept (b)

The slope - intercept form of a line is \( y=mx + b \). When \( x = 0 \), from the table, \( y=-2 \). Substituting \( x = 0 \), \( y=-2 \) and \( m=\frac{17}{2}\) into \( y=mx + b \), we get:
\(-2=\frac{17}{2}(0)+b\), so \( b=-2 \)

Step3: Write the equation

Using the slope - intercept form \( y = mx + b \) with \( m=\frac{17}{2}\) and \( b=-2 \), the equation is \( y=\frac{17}{2}x-2 \) or \( y = 8.5x-2 \)

Answer:

\( m:\frac{17}{2}\) (or \( 8.5 \)), \( b:-2 \), equation: \( y = 8.5x-2 \) (or \( y=\frac{17}{2}x - 2\))