004 Sample Final A, Problem 14 - Revision history

MathAdmin at 17:22, 2 June 2015

2015-06-02T17:22:58Z

MathAdmin at 17:22, 2 June 2015

2015-06-02T17:22:40Z

MathAdmin: Created page with " a) Find an equation of the line passing through (-4, 2) and (3, 6).
b) Find the slope of any line perpendicular to your answer from a) {| class="mw-col..."

2015-06-01T05:49:59Z

Created page with " a) Find an equation of the line passing through (-4, 2) and (3, 6). b) Find the slope of any line perpendicular to your answer from a) {| class="mw-col..."

New page

a) Find an equation of the line passing through (-4, 2) and (3, 6). 
b) Find the slope of any line perpendicular to your answer from a)
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Foundations
|-
|1) How do you find the slope of a line through points <math>(x_1,y_1)</math> and <math>(x_2,y_2)</math>?
|-
|2) What is the equation of a line?
|-
|3) How do you find the slope of a line perpendicular to a line <math> y </math>?
|-
|Answer:
|-
|1) The slope is given by <math>m=\frac{y_2-y_1}{x_2-x_1} </math>.
|-
|2) The equation of a line is <math>y-y_1=m(x-x_1)</math> where <math>(x_1,y_1)</math> is a point on the line.
|-
|3) The slope is given by <math>-\frac{1}{m}</math> where <math>m</math> is the slope of the line <math>y</math>.
|}

Solution:

{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
|-
|Using the above equation, the slope is equal to <math> m=\frac{6-2}{3-(-4)}=\frac{4}{7}</math>.
|-
|
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
|-
|The equation of the line is <math> y-6=\frac{4}{7}(x-3)</math>. Solving for <math>y</math>,
|-
|we get <math>y=\frac{4}{7}x+\frac{30}{7}</math>.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 3:
|-
|The slope of any line perpendicular to the line in Step 2 is <math>-\frac{1}{(\frac{4}{7})}=-\frac{7}{4}</math>.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answer:
|-
| The slope is <math> \frac{4}{7}</math>, the equation of the line is <math>y=\frac{4}{7}x+\frac{30}{7}</math>, and
|-
|the slope of any line perpendicular to this line is <math>-\frac{7}{4}</math>.
|}

[[004 Sample Final A|'''Return to Sample Exam''']]

@@ Line 1: / Line 1: @@
- <span class="exam"> a) Find an equation of the line passing through (-4, 2) and (3, 6).<br>
+<span class="exam"> a) Find an equation of the line passing through (-4, 2) and (3, 6).</span> <br>
- <span class="exam"> b) Find the slope of any line perpendicular to your answer from a)
+<span class="exam"> b) Find the slope of any line perpendicular to your answer from a)
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 ! Foundations

@@ Line 1: / Line 1: @@
-<span class="exam"> a) Find an equation of the line passing through (-4, 2) and (3, 6).<br>
+ <span class="exam"> a) Find an equation of the line passing through (-4, 2) and (3, 6).<br>
-b) Find the slope of any line perpendicular to your answer from a)
+ <span class="exam"> b) Find the slope of any line perpendicular to your answer from a)
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 ! Foundations

004 Sample Final A, Problem 14 - Revision history

MathAdmin at 17:22, 2 June 2015

MathAdmin at 17:22, 2 June 2015

MathAdmin: Created page with " a) Find an equation of the line passing through (-4, 2) and (3, 6). b) Find the slope of any line perpendicular to your answer from a) {| class="mw-col..."

MathAdmin: Created page with " a) Find an equation of the line passing through (-4, 2) and (3, 6).
b) Find the slope of any line perpendicular to your answer from a) {| class="mw-col..."