Question

use the graph, given above, to find the slope and equation for the line.
a) slope of the line: ( m = -\frac{3}{2} )

b) the equation of the line in slope - intercept form: ( y = -\frac{2}{3}x + 1 )

assume the vertical axis is ( y ) and the horizontal axis is ( x ).

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0,1)$, so $b=1$.

Step2: Confirm slope

Use two points, e.g., $(0,1)$ and $(2,-2)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-2-1}{2-0}=\frac{-3}{2}$

Step3: Write slope-intercept equation

Slope-intercept form: $y=mx+b$. Substitute $m=-\frac{3}{2}$ and $b=1$.
$y=-\frac{3}{2}x+1$

Answer:

a) $m=-\frac{3}{2}$
b) $y=-\frac{3}{2}x+1$