Question

graph the line with slope $-1$ passing through the point $(-2, 4)$.

Explanation:

Step1: Find line equation (point-slope)

Use point-slope form: $y - y_1 = m(x - x_1)$
Substitute $m=-1$, $x_1=-2$, $y_1=4$:
$y - 4 = -1(x - (-2))$

Step2: Simplify to slope-intercept form

Simplify the equation:
$y - 4 = -x - 2$
$y = -x + 2$

Step3: Identify second point

Use slope $-1 = \frac{\Delta y}{\Delta x} = \frac{-1}{1}$. From $(-2,4)$, move 1 right, 1 down:
$(-2+1, 4-1) = (-1, 3)$

Step4: Plot and connect points

Plot $(-2,4)$ and $(-1,3)$, then draw a straight line through them, extending across the grid.

Answer:

The line is defined by the equation $y = -x + 2$, passing through $(-2, 4)$ and other points like $(-1, 3)$, $(0, 2)$, $(1, 1)$, etc. When graphed, it is a downward-sloping line crossing the y-axis at $(0,2)$.