Question

click a line to delete it (image of a coordinate plane with a line and points)

Explanation:

Step1: Identify two points

From the graph, we can see two points: \((-10, 7.5)\) (approximate) and \((-1, -4)\), and also it crosses the x - axis at \((-4, 0)\). Let's use two clear points, say \((-10, 7.5)\) and \((-4, 0)\) (or we can use \((-1, -4)\) and \((-10, 7.5)\)). Let's take \((x_1,y_1)=(-10, 7.5)\) and \((x_2,y_2)=(-4, 0)\)

Step2: Calculate the slope

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
Substitute the values: \(m=\frac{0 - 7.5}{-4-(-10)}=\frac{-7.5}{6}=- 1.25=-\frac{5}{4}\)

Step3: Use point - slope form

Using the point \((-4,0)\), the point - slope form is \(y - y_1=m(x - x_1)\)
\(y-0 =-\frac{5}{4}(x + 4)\)
Simplify: \(y=-\frac{5}{4}x-5\)

If we use the point \((-1,-4)\):
\(m=\frac{-4 - 7.5}{-1-(-10)}=\frac{-11.5}{9}\approx - 1.28\) (close to \(-\frac{5}{4}=-1.25\) due to approximation of the first point). But with exact calculation, if we take the two clear points (assuming the first point is \((-10,7.5)\) as per the grid, each square is 1 unit). Wait, maybe the first point is \((-10,7.5)\) (since at x=-10, y is 7.5) and the second point is \((-1,-4)\). Let's recalculate slope: \(m=\frac{-4 - 7.5}{-1+10}=\frac{-11.5}{9}\approx - 1.28\), but maybe the intended points are \((-10,7.5)\) and \((-4,0)\) or \((-10,7.5)\) and \((0, - 5)\) (since when x = 0,y=-5). Let's check with x = 0, from the line, y=-5. So the y - intercept \(b=-5\) and slope \(m =-\frac{5}{4}\), so the equation is \(y =-\frac{5}{4}x-5\)

Answer:

The equation of the line is \(y =-\frac{5}{4}x - 5\) (or in decimal form \(y=-1.25x - 5\))