Question

question 1-2
what is the y-intercept of the line that passes through the points, $(-1, 10)$ and $(2, 1)$?
$\circ$ $-1$
$\circ$ $3$
$\circ$ $7$
$\circ$ $9$

Explanation:

Step1: Find the slope of the line

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Using the points \((-1, 10)\) and \((2, 1)\), we have \( x_1=-1,y_1 = 10,x_2=2,y_2=1 \).
So \( m=\frac{1 - 10}{2-(-1)}=\frac{-9}{3}=- 3 \).

Step2: Use point - slope form to find the equation of the line

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \((2,1)\) and \( m=-3 \).
\( y - 1=-3(x - 2) \)
Expand the right - hand side: \( y-1=-3x + 6 \)
Add 1 to both sides to get the slope - intercept form \( y=mx + b \) (where \( b \) is the y - intercept): \( y=-3x+7 \)

Answer:

7