Question

writing equations between 2 points
write an equation in slope intercept form that passes through
the two points shown:
(-8,-2) and (2,3)
y = mx + b

Explanation:

Step1: Calculate the slope \( m \)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
Given points \((-8, -2)\) and \((2, 3)\), so \( x_1 = -8 \), \( y_1 = -2 \), \( x_2 = 2 \), \( y_2 = 3 \).
\( m = \frac{3 - (-2)}{2 - (-8)} = \frac{3 + 2}{2 + 8} = \frac{5}{10} = \frac{1}{2} \)

Step2: Find the y-intercept \( b \)

Use the slope-intercept form \( y = mx + b \) and one of the points, say \((2, 3)\) (we can also use \((-8, -2)\)).
Substitute \( m = \frac{1}{2} \), \( x = 2 \), \( y = 3 \) into \( y = mx + b \):
\( 3 = \frac{1}{2}(2) + b \)
\( 3 = 1 + b \)
Subtract 1 from both sides: \( b = 3 - 1 = 2 \)

Step3: Write the equation

Now that we have \( m = \frac{1}{2} \) and \( b = 2 \), substitute into \( y = mx + b \):
\( y = \frac{1}{2}x + 2 \)

Answer:

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