I don't understand how to find an equation or how my answers are supposed to be slope-intercept

Question

Find an equation of the line that satisfies the given conditions. Your answers should be in slope-intercept
form.
a) x-intercept of -8; y-intercept of 6
b) Through (1,1) and perpendicular to the line 4x − 8y = 1
c) Through (4,5), and parallel to the y-axis

Answer 1

PART A:

 

X-intercept: where the line crosses the x-axis and y=0.

So if the x-intercept is -8, then (-8,0) must be on the line.

 

Y-intercept: where the line crosses the y-axis and x=0.

So if the y-intercept is 6, then (0,6) must be on the line.

 

the slope is (6-0)/(0 - -8) = 6/8 = 3/4

The equation of this line is then y = 3/4X + 6

 

 

PART B:

 

    The given line is 4x - 8y = 1

                          4x - 1 = 8y

 

                         1/2X - 1/8 = y

    The slope of the given line is M=1/2

 

 Perpendicular lines have slopes that are NEGATIVE RECIPROCALS.

 So the perpendicular line has slope -2.

y = M x + b

(1,1)--> x=1 and y =1; together with M=-2, it is:

  1 = (-2)(1) + b

  1 = -2 + b

  b = 3

 

The equation of the line perpendicular to 4x-8y=1 passing through (1,1) is y = -2x + 3

 

PART C:

 

  The slope does not exist (is undefined) is it is parallel to the y-axis.

   It is a VERTICAL LINE.  Since (4,5) is on it, the equation is simply x=4 

 (y can be anything)

 

You need to graph the lines on graph paper as you read along.