Graphing a Line

A linear function is represented by the table below.  Draw a line on the coordinate grid that has a greater
y-intercept than the function represented by the table and is perpendicular to the function y + (1/4)x = 2.

 x      y 
-1     -6
 1     -2
 3      2

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Find the slope of the line represented by the given table.

y2 - y1
---------- = slope of a line
x2 - x1

(-1,-6) and (1,-2) are two given points.

-2 - (-6)
---------- = slope of the line given by the table   {substituted coordinates into slope formula}
1 - (-1)

4
--- = slope of the line   {simplified in numerator and denominator}
2

slope = 2


Find the y-intercept of the line represented by the given table.

Slope-intercept form is y = mx + b
m is the slope
b is the y-intercept

(-1,-6) and m = 2 are a point and slope of the line represented by the given table.

-6 = 2(-1) + b   {substituted point and slope into slope-intercept form}
-6 = -2 + b   {multiplied 2 by -1}
b = -4   {added 2 to each side}


Find the slope that is perpendicular to the line represented by the given equation.

Perpendicular lines have slopes which are negative reciprocals.

The given equation is y + (1/4)x = 2.
y = (-1/4)x + 2   {subtracted (1/4)x from each side}
slope = -1/4   {slope-intercept form is y = mx + b, where m is the slope}
perpendicular slope is 4   {perpendicular lines have slopes which are negative reciprocals}


A line that has a greater y-intercept than the line represented by the given table and perpendicular 
to the line y + (1/4)x = 2 could be:

y = 4x + 1

To graph:
- put a point on 1 on the y-axis   {1 is the y-intercept of this line}
- from there, move up 4 and to the right 1 and put another point   {slope is 4, thus rise is 4 and run is 1}

Ask Algebra House
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