Question

1. write the equation of the line that passes through (3,5) and (10, -9)

type a response
a.6.b

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1, y_1) = (3, 5)$ and $(x_2, y_2) = (10, -9)$. Then $m = \frac{-9 - 5}{10 - 3} = \frac{-14}{7} = -2$.

Step2: Use point - slope form

The point - slope form of a line is $y - y_1 = m(x - x_1)$. Using the point $(3, 5)$ and $m=-2$, we have $y - 5=-2(x - 3)$.

Step3: Simplify to slope - intercept form

Expand the right - hand side: $y - 5=-2x + 6$. Then add 5 to both sides: $y=-2x+6 + 5$, so $y=-2x + 11$. We can also write it in standard form $2x+y=11$.

Answer:

The equation of the line is $y = - 2x+11$ (or $2x + y=11$)