Question

lesson extra practice:
writing equations in slope-intercept form
write an equation of the line given by the graph or table.
1.
2.
3.
4.
x | y
-2 | 11
0 | 5
2 | -1
4 | -7
5.
x | y
-4 | -2
0 | -1
4 | 0
8 | 1
6.
x | y
-5 | 1
-5 | 3
-5 | 5
-5 | 7
write an equation of the line that passes through the given points.

1. (0, 0), (4, -2)
2. (-2, 6), (0, 3)
3. (1, 4), (6, 4)

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practice workbook: lesson and standards - based practice
grade 8 41

Explanation:

Step1: Identify the slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For the points \((0,0)\) and \((4, - 2)\), \(x_1 = 0,y_1 = 0,x_2=4,y_2=-2\).
So \(m=\frac{-2 - 0}{4 - 0}=\frac{-2}{4}=-\frac{1}{2}\).

Step2: Use slope - intercept form

The slope - intercept form of a line is \(y=mx + b\), where \(b\) is the y - intercept. Since the line passes through \((0,0)\), when \(x = 0,y = 0\). Substituting \(m=-\frac{1}{2}\) and \((x,y)=(0,0)\) into \(y=mx + b\), we get \(0=-\frac{1}{2}(0)+b\), so \(b = 0\).

Step3: Write the equation

Substituting \(m =-\frac{1}{2}\) and \(b = 0\) into \(y=mx + b\), the equation of the line is \(y=-\frac{1}{2}x\).

Answer:

\(y =-\frac{1}{2}x\)