Easy Algebra Step-by-Step

Graphing Linear Equations 185

If you have two distinct points (,xy,,y 1 ) and (,xy,,y 2 ) on a nonvertical line,

then the slope, m, of the line is given by the ratio m

yy

xx

=^1

y

21 x

. If the slope

is negative, the line is slanting down as you move from left to right. If the

slope is positive, the line is slanting up as you move from left to right. And if

the slope is 0, the line is a horizontal line.

Problem Find the slope of the line that passes through the points (,, 6 )

and (3,7).

Solution

Step 1. Use the slope ratio formula to fi nd the slope.

m

yy

xx

= = =

−

(^1) =−
y
21 x

67 −

43 −

1

1

1

When you graph linear equations “by hand,” you put the equation in the

slope-y-intercept form and then set up an x-y T-table (illustrated below) to

compute point values for the graph.

Problem Graph the line whose equation is yx 21 xx=−.

Solution

Step 1. Put the equation in slope-y-intercept form by solving for y.

yx 21 xx=−

yx^22 x+ xx^12 +

yx 12 +

yx^21 xx−

Step 2. Set up an x-y T-t able.

x yx 21 xx−

Step 3. Because two points determine a line, substitute two convenient

values for x and compute the corresponding y values.

x yx 21 xx−

0−1

11