Question

enter your answer in the box.
y = \square x - \square

Explanation:

Step1: Identify two points on the line

We can see two points: \((-1, 2)\) and \((0, -3)\) (the y - intercept).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(-1,2)\) and \((x_2,y_2)=(0, - 3)\), we have \(m=\frac{-3 - 2}{0-(-1)}=\frac{-5}{1}=-5\).

Step3: Determine the y - intercept \(b\)

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,-3)\), we know that \(b=-3\), but the equation is in the form \(y=mx - c\) (rewriting \(y=mx + b\) as \(y=mx-(-b)\) if \(b\) is negative). Wait, the given form is \(y=\square x-\square\). The slope \(m=-5\), and the y - intercept \(b=-3\), so the equation is \(y=-5x - (- 3)\)? No, wait, let's re - examine. Wait, the two points: when \(x=-1\), \(y = 2\); when \(x = 0\), \(y=-3\). The slope \(m=\frac{-3 - 2}{0 - (-1)}=\frac{-5}{1}=-5\). The equation of a line is \(y=mx + b\). Substituting \(x = 0\), \(y=-3\), we get \(b=-3\). But the given form is \(y=\square x-\square\). So \(y=-5x-(-3)\)? No, that's not right. Wait, maybe I made a mistake in the points. Wait, another point: let's check the graph again. The line passes through \((-1,2)\) and \((0, - 3)\)? Wait, no, when \(x = 0\), the point is \((0,-3)\), and when \(x=-1\), the point is \((-1,2)\). Let's use the slope formula again. \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2-(-3)}{-1 - 0}=\frac{5}{-1}=-5\). The equation is \(y=-5x + b\). Substitute \(x=-1\), \(y = 2\): \(2=-5\times(-1)+b\), \(2 = 5 + b\), so \(b=2 - 5=-3\). So the equation is \(y=-5x-3\)? Wait, no, \(y=-5x-3\) is \(y=-5x+(-3)\). But the given form is \(y=\square x-\square\). So if we write \(y=-5x-3\), the first box is \(-5\) and the second box is \(3\) (because \(y=-5x-3\) is equivalent to \(y=-5x-(3)\)). Wait, let's verify with \(x=-1\): \(y=-5\times(-1)-3=5 - 3 = 2\), which matches the point \((-1,2)\). And with \(x = 0\): \(y=-5\times0-3=-3\), which matches the point \((0,-3)\). Yes, that works.

Answer:

The first box is \(-5\) and the second box is \(3\), so \(y=-5x - 3\) (i.e., \(y=\boldsymbol{-5}x-\boldsymbol{3}\))