Graphing Horizontal and Vertical Lines

a

We should find the slope and the $y$ -intercept and for this we have a special form, the slope-intercept form. $y = m x + b,$ In the above equation, $m$ represents the slope and $b$ the $y -$ intercept of the line. Let's rewrite our equation a little bit so that it more closely resembles this form. It will make it easier to identify the slope and intercept. $y = \frac{1}{2} \Leftrightarrow y = 0 x + \frac{1}{2}$ We see above that the slope is $0$ and the $y -$ intercept is $\frac{1}{2} .$

b

Since we know two points on the line, we can use the slope formula to find its slope.

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

We are given the points

(- 2, 2)

and

(- 6, 2) .

Note that, when substituting these values into the slope formula, it doesn't matter which point we choose to use as

(x_{1}, y_{1})

or

(x_{2}, y_{2}),

both will give the same result.

m = \frac{2 - 2}{- 2 - ( - 6 )} or m = \frac{- 2 - 2}{- 6 - ( - 2 )}

Here, we will use the points in the given order and solve for

m .

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

SubstitutePointsSubstitute

(- 2, 2)

&

(- 6, 2)

m = \frac{2 - 2}{- 2 - ( - 6 )}

Evaluate right-hand side

SubNeg

a - (- b) = a + b

m = \frac{2 - 2}{- 2 + 6}

AddSubTermsAdd and subtract terms

m = \frac{0}{4}

CalcQuotCalculate quotient

m = 0

The slope of the line that passes through the given points is

0 .

This means that as

x

increases,

y

neither increases nor decreases. The graph will be a horizontal line and has the same

y

-value for all points. Thus, the

y

-intercept will be at

y = 2 .

Graphing Horizontal and Vertical Lines 1.5 - Solution