Question

Find the equation of a line
(1)with slope -2 and y-intercept
5.
(2) with slope-1/3 and Y intersect -4
(3)with slope -3 and intersecting the X-axis at distance of 4units to left of origin.
(4)which cuts off an intercepts of length of length 3 on Y-axis and having slope 5.
(5)intersecting Y-axis at a distance of 2units above the origin and making an angle of 30° with positive direction of X-axis.
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Answer 1

Step-by-step explanation:

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Answer 2

Q1) Slope= -2

y- intercept= 5

y=mx+c slope : m , y or x- intercept : c !

y= -2x+5

Standard form: 2x+y-5=0

Q2) y=mx+c

y= -1/3x + (-4) (see ! )

y= -x/3 -4 (multiply 3 both sides)

3y= -x -12

Standard form: x+3y+12=0

Q3)m= -3

c= 4 units left of origin

=4 units left of (0,0)

= (-4,0)

x- intercept= -4

y= -3x+ (-4)

y= -3x-4

Standard form: 3x+y+4=0

Q4) For finding slope(m):

slope gradient = 30°

tan theta=m

tan 30 = 1/√3

m= 1/√3

For finding y- intercept:

2 units above origin

2 units above (0,0)

c= (0,2)

c=2

y=mx+c

y=1/√3 *x + 2

√3y = x + 2√3 (multiply √3 both sides)

Standard form: x-√3y+2√3