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Question 1112005: 1. Given the linear equation : -3x + 5y = 15
a. Show and explain the process to find the x and y intercepts
b. Use the x- and y-intercepts found in part a and the slope formula to find the slope. Show all work.
c. Begin with the form -3x+5y=15 and write the equation in slope intercept form. Show all work.
d. Based on the slope-intercept form of the line, what are the slope and y-intercept ? Are these values consistent with answers in parts a and b ?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! a.
For  ,  , and solving for  we find
 and  for the x-intercept.
For  ,  , and solving for  we find
 and  for the y-intercept.
The points called x-intercept and y-intercept are
 and  respectively.
EXPLANATION:
The x-intercept sometimes means the point where the line intersects the x-axis,
but as for all points of the x-axis, that intersection point has
so its x-coordinate is also called the x-intercept of the line.
Similarly, the point (with ) , or just its y-coordinate is called the y-intercept.
b.
Maybe you were taught that the slope of a line going through points  and  is
 .
Applied to the points found in part a,
 .
So,  .
c.
There is an infinite number of equivalent equations that represent the same line as  ,
but there is only one that starts with "y=", and that is the slope-intercept form.
To get it, we just solve for y:
 .
d.
The slope-intercept form of the equation of a line is an equation of the form
 where the constants and 
are the slope and y-intercept of the line respectively.
The equation  found in part c,
tells us That  is the slope (as found in part b),
and that  is the y-intercept (as found in part a).
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