Question

you may complete the assignment on the worksheet or on lined paper.
write the equation of the line in slope-intercept form.
1.
equation:
2.
equation:
3.
equation:
4.
equation:
5.
equation:
6.
equation:

Explanation:

Problem 1:

Step1: Identify slope and intercept

The line passes through \((-2, 1)\), \((0, -1)\), \((2, -3)\). Slope \(m=\frac{-1 - 1}{0 - (-2)}=\frac{-2}{2}=-1\). Y - intercept \(b=-1\).

Step2: Write slope - intercept form

Slope - intercept form is \(y = mx + b\). Substituting \(m=-1\) and \(b = - 1\), we get \(y=-x - 1\).

Step1: Identify slope and intercept

The line passes through \((-4, 1)\), \((0, 0)\), \((4, -1)\). Slope \(m=\frac{0 - 1}{0 - (-4)}=\frac{-1}{4}=-\frac{1}{4}\)? Wait, no, from \((-4,1)\) to \((4, - 1)\), change in \(y=-1 - 1=-2\), change in \(x = 4-(-4)=8\), so \(m=\frac{-2}{8}=-\frac{1}{4}\)? Wait, no, looking at the graph, the line passes through \((-4,1)\) and \((4, - 1)\)? Wait, actually, the line passes through \((-4,1)\) and \((4, - 1)\)? Wait, no, the origin \((0,0)\) is on the line. Let's take two points: \((-4,1)\) and \((0,0)\). Slope \(m=\frac{0 - 1}{0 - (-4)}=-\frac{1}{4}\)? Wait, no, maybe I made a mistake. Wait, the line goes from \((-4,1)\) to \((4, - 1)\), so the slope is \(\frac{-1 - 1}{4-(-4)}=\frac{-2}{8}=-\frac{1}{4}\). Y - intercept \(b = 0\).

Step2: Write slope - intercept form

Using \(y=mx + b\), with \(m =-\frac{1}{4}\) and \(b = 0\), we get \(y=-\frac{1}{4}x\). Wait, but maybe the grid is with 1 - unit squares. Let's re - check. If the points are \((-4,1)\) and \((4, - 1)\), the slope is \(-\frac{1}{4}\), but maybe the correct points are \((-3,1)\) and \((3, - 1)\)? Wait, the graph: let's assume each grid is 1 unit. The line passes through \((-4,1)\) and \((4, - 1)\), so slope \(m=\frac{-1 - 1}{4-(-4)}=-\frac{2}{8}=-\frac{1}{4}\), and \(b = 0\). So equation is \(y=-\frac{1}{4}x\). Wait, but maybe I misread the points. Alternatively, if the line passes through \((-2,1)\) and \((2, - 1)\), slope is \(\frac{-1 - 1}{2-(-2)}=\frac{-2}{4}=-\frac{1}{2}\). Oh, maybe the grid is 2 - unit? Wait, the problem is to write the equation in slope - intercept form. Let's take the two points: for the second graph, let's say the left point is \((-4,1)\) and the right point is \((4, - 1)\), so slope \(m=-\frac{1}{4}\), \(b = 0\), so \(y=-\frac{1}{4}x\). But maybe the correct slope is \(-\frac{1}{3}\)? No, let's do it properly. Let's take two clear points. The line passes through \((-4,1)\) and \((0,0)\). So slope \(m=\frac{0 - 1}{0 - (-4)}=-\frac{1}{4}\), and \(b = 0\). So equation is \(y=-\frac{1}{4}x\).

Step1: Identify slope and intercept

The line passes through \((-4,2)\), \((0,1)\), \((4,0)\). Slope \(m=\frac{1 - 2}{0 - (-4)}=\frac{-1}{4}=-\frac{1}{4}\). Y - intercept \(b = 1\).

Step2: Write slope - intercept form

Using \(y=mx + b\), with \(m=-\frac{1}{4}\) and \(b = 1\), we get \(y=-\frac{1}{4}x + 1\).

Answer:

\(y=-x - 1\)

Problem 2: