question what is an equation of the line that passes through the points (3, 3) and (-3, 7)? answer attempt 1…

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, $(x_1,y_1)=(3,3)$ and $(x_2,y_2)=(-3,7)$. So $m=\frac{7 - 3}{-3 - 3}=\frac{4}{-6}=-\frac{2}{3}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(3,3)$ and $m =-\frac{2}{3}$, we have $y - 3=-\frac{2}{3}(x - 3)$.

Step3: Simplify the equation

Expand the right - hand side: $y - 3=-\frac{2}{3}x+2$. Then add 3 to both sides to get the slope - intercept form $y=-\frac{2}{3}x + 5$. We can also write it in general form. Multiply through by 3 to get $3y=-2x + 15$, or $2x+3y=15$.

Answer:

$y =-\frac{2}{3}x + 5$ (or $2x + 3y=15$)