the table represents a linear equation. which equation correctly uses point $(-2,-6)$ to write the equation…

the table represents a linear equation. which equation correctly uses point $(-2,-6)$ to write the equation of this line in point - slope form? $y - 6=\frac{5}{2}(x - 2)$ $y - 6=\frac{2}{5}(x - 2)$ $y + 6=\frac{2}{5}(x + 2)$ $y + 6=\frac{5}{2}(x + 2)$

the table represents a linear equation. which equation correctly uses point $(-2,-6)$ to write the equation of this line in point - slope form? $y - 6=\frac{5}{2}(x - 2)$ $y - 6=\frac{2}{5}(x - 2)$ $y + 6=\frac{2}{5}(x + 2)$ $y + 6=\frac{5}{2}(x + 2)$

Answer

Explanation:

Step1: Calculate the slope

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Let's take two points ((x_1,y_1)=(-4,-11)) and ((x_2,y_2)=(6,14)). [ \begin{align*} m&=\frac{14-(-11)}{6-(-4)}\ &=\frac{14 + 11}{6+4}\ &=\frac{25}{10}\ &=\frac{5}{2} \end{align*} ]

Step2: Use the point - slope form

The point - slope form is (y - y_0=m(x - x_0)), where ((x_0,y_0)=(-2,-6)) and (m = \frac{5}{2}). Substitute (x_0=-2), (y_0=-6) and (m=\frac{5}{2}) into the formula: [ \begin{align*} y-(-6)&=\frac{5}{2}(x-(-2))\ y + 6&=\frac{5}{2}(x + 2) \end{align*} ]

Answer:

(y + 6=\frac{5}{2}(x + 2)) (the fourth option)