# 12.1, 12.2 Linear Equations and Scatter Plots

# Problem 1

The following is a graph of a line:

Write the equation of the line [latex]y=[/latex]

## Correct Answers

2x + 3

# Problem 2

The following is a graph of a line:

Write the equation of the line [latex]y=[/latex]

## Solution

A line’s slope-intercept equation has the form *y *= *mx *+ *b*, where *m *is the slope and *b *is the *y*-intercept. We first find the slope.

To find the slope of a line from its graph, we identify two points, and then draw a slope triangle. It’s wise to choose points with integer coordinates. For this problem, we choose (0, 1) and (9, −5).

Next, we draw a slope triangle and find the “rise” and “run”. In this problem, the rise is *−*6 and the run is 9.

[latex]slope=\frac{rise}{run}[/latex]

[latex]=\frac{-6}{9}[/latex]

[latex]=-\frac{2}{3}[/latex]

This line’s slope is –[latex]\frac{2}{3}[/latex].

It’s clear in the graph that this line’s *y*-intercept is (0*, *1).

So this line’s slope-intercept equation is [latex]y=-\frac{2}{3}x+1[/latex]

## Correct Answers

-0.666667x+1