Question

for #’s 12 and 13, write an equation of the line given by the graph or table.
12)
graph of a line passing through (0, 2) and (5, 5)
13)

x	y
2	-1
4	-7
6	-13

Explanation:

Problem 12

Step1: Identify slope and y-intercept

The line passes through \((0, 2)\) (y-intercept \(b = 2\)) and \((5, 5)\). Slope \(m=\frac{5 - 2}{5 - 0}=\frac{3}{5}\).

Step2: Write slope - intercept form

Slope - intercept form is \(y=mx + b\). Substitute \(m=\frac{3}{5}\) and \(b = 2\). So \(y=\frac{3}{5}x+2\).

Step1: Find y - intercept and slope

From the table, when \(x = 0\), \(y = 5\), so \(b = 5\). Take two points \((0,5)\) and \((2,-1)\). Slope \(m=\frac{-1 - 5}{2 - 0}=\frac{-6}{2}=-3\).

Step2: Write the equation

Using \(y=mx + b\), substitute \(m=-3\) and \(b = 5\). So \(y=-3x + 5\).

Answer:

\(y=\frac{3}{5}x + 2\)

Problem 13