write an equation of the line that passes through the pair of points. (9, 2), (-2, 6)

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(9,2)$ and $(x_2,y_2)=(-2,6)$. So $m=\frac{6 - 2}{-2 - 9}=\frac{4}{-11}=-\frac{4}{11}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Let's use the point $(9,2)$ and $m = -\frac{4}{11}$. Then $y - 2=-\frac{4}{11}(x - 9)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y - 2=-\frac{4}{11}x+\frac{36}{11}$. Add 2 to both sides: $y=-\frac{4}{11}x+\frac{36}{11}+2$. Since $2=\frac{22}{11}$, we have $y=-\frac{4}{11}x+\frac{36 + 22}{11}=-\frac{4}{11}x+\frac{58}{11}$.

Step4: Convert to general form

Multiply through by 11 to get $11y=-4x + 58$. Rearrange to $4x+11y=58$.

Answer:

$4x + 11y=58$