Question

write an equation of the line below.

Explanation:

Step1: Identify two points on the line

From the graph, we can see two points: \((-3, 6)\) and \((0, -2)\) (the y - intercept).

Step2: Calculate the slope (m)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-3,6)\) and \((x_2,y_2)=(0,-2)\). Then \(m=\frac{-2 - 6}{0-(-3)}=\frac{-8}{3}\)? Wait, no, wait. Wait, if we take \((0,-2)\) and \((-3,6)\), \(y_2 - y_1=6-(-2)=8\), \(x_2 - x_1=-3 - 0=-3\), so \(m=\frac{8}{-3}=-\frac{8}{3}\)? Wait, no, maybe I picked the wrong points. Wait, the y - intercept is at \((0,-2)\), and another point: let's check the grid. Wait, when \(x = - 3\), \(y = 6\)? Wait, no, maybe I misread. Wait, the blue dot: let's see the x - coordinate of the blue dot is - 4? Wait, no, the x - axis: from left, - 8, - 7, - 6, - 5, - 4, - 3, - 2, - 1, 0, 1,... The blue dot is at x=-4? Wait, no, the first blue dot: let's count the grid. Wait, the vertical lines: each grid is 1 unit. So the point with the blue dot: x=-4, y = 6? Wait, no, when x=-4, y=6? And the other point is (0,-2). Let's recalculate the slope. \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-2 - 6}{0-(-4)}=\frac{-8}{4}=-2\). Ah, I see, I misread the x - coordinate of the first point. So the two points are \((-4,6)\) and \((0,-2)\).

So \(m=\frac{-2 - 6}{0 - (-4)}=\frac{-8}{4}=-2\).

Step3: Use the slope - intercept form \(y=mx + b\)

The slope - intercept form is \(y=mx + b\), where \(b\) is the y - intercept. We know \(b=-2\) (from the point \((0,-2)\)) and \(m=-2\). So the equation is \(y=-2x-2\). Let's check with the point \((-4,6)\): \(y=-2\times(-4)-2 = 8 - 2=6\), which matches.

Answer:

\(y=-2x - 2\)