Question

1. write an equation of the line that passes through each pair of points.

a. (-3, -3), (0, 6)
b. (-2, 5), (3, -4

Explanation:

Part a:

Step1: Find the slope ($m$)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $(-3, -3)$ and $(0, 6)$, let $(x_1, y_1) = (-3, -3)$ and $(x_2, y_2) = (0, 6)$. Then $m = \frac{6 - (-3)}{0 - (-3)} = \frac{9}{3} = 3$.

Step2: Use the y - intercept form ($y = mx + b$)

We know that when $x = 0$, $y = 6$ (from the point $(0, 6)$), so the y - intercept $b = 6$. Substituting $m = 3$ and $b = 6$ into $y = mx + b$, we get $y = 3x + 6$.

Step1: Find the slope ($m$)

Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ with points $(-2,5)$ and $(3, - 4)$. Let $(x_1,y_1)=(-2,5)$ and $(x_2,y_2)=(3, - 4)$. Then $m=\frac{-4 - 5}{3-(-2)}=\frac{-9}{5}=-\frac{9}{5}$.

Step2: Use the point - slope form or find $b$

We can use the slope - intercept form $y = mx + b$. Substitute one of the points, say $(-2,5)$ and $m = -\frac{9}{5}$ into $y=mx + b$:
$5=-\frac{9}{5}\times(-2)+b$
$5=\frac{18}{5}+b$
Subtract $\frac{18}{5}$ from both sides: $b = 5-\frac{18}{5}=\frac{25 - 18}{5}=\frac{7}{5}$.
So the equation is $y=-\frac{9}{5}x+\frac{7}{5}$.

Answer:

$y = 3x + 6$

Part b: (assuming the second point is $(3, - 4)$ as it seems to be cut off)