Question

what is the equation of the line that passes through the points (9, -2) and (12, 4)? write your answer in slope-intercept form.
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Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For the points \( (9,-2) \) and \( (12,4) \), we have \( x_1 = 9,y_1=-2,x_2 = 12,y_2 = 4 \). So \( m=\frac{4-(-2)}{12 - 9}=\frac{4 + 2}{3}=\frac{6}{3}=2 \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \( (9,-2) \) and \( m = 2 \). Substituting these values, we get \( y-(-2)=2(x - 9) \), which simplifies to \( y + 2=2x-18 \).

Step3: Convert to slope - intercept form

Slope - intercept form is \( y=mx + b \). From \( y + 2=2x-18 \), subtract 2 from both sides: \( y=2x-18 - 2 \), so \( y=2x-20 \).

Answer:

\( y = 2x-20 \)