10TH GRADE MATH SOLUTION EXERCISE 5.4 PART1

About "10th grade math solution exercise 5.4 part1"

Question 1 :

Write the equations of the straight lines parallel to x- axis which are at a distance of 5 units from the x-axis.

Solution :

Question 2 :

Find the equations of the straight lines parallel to the coordinate axes and passing through the point (-5,-2).

Solution :

If we draw a line parallel to x-axis then the particular line will pass through the point -2 on y axis. 

Equation of the line parallel to x-axis is y = -2

If we draw a line parallel to y-axis then the particular line will pass through the point -5 on x axis. 

Equation of the line parallel to y-axis is x = -5

Question  3 :

Find the equation of a straight line whose

(i) slope is -3 and y-intercept is 4.

Solution :

Slope (m) = -3

y-intercept (c) = 4

Equation of the line :

y = mx + c

y = -3x + 4

(ii) angle of inclination is 60° and y-intercept is 3.

Solution :

Slope (m) = tan 60° √3

y-intercept (c) = 3

Equation of the line :

y = mx + c

y = √3 x + 3 

Question 4 :

Find the equation of the line intersecting the y- axis at a distance of 3 units above the origin and tan θ = 1/2, where θ is the angle of inclination.

Solution :

Slope (m) = tan  θ = 1/2

Since the line line intersecting the y- axis at a distance of 3 units above the origin, one of the points on the line is (0, 3)

Equation of the line :  

(y - y₁)  =  m (x - x₁)

(y - 3)  =  (1/2) (x - 0) 

2(y - 3)  =  1 (x) 

2y - 6 = x 

x - 2y + 6 = 0

Hence the required equation of the line is x - 2y + 6 = 0.

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