Students often refer to NCERT Class 9 Advanced Maths Solutions Chapter 4 Coordinate Geometry Ex 4.5 to verify their answers.
Advanced Maths Class 9 Exercise 4.5 Solutions
Class 9 Advanced Maths Ex 4.5 Solutions
Question 1.
A straight line crosses the y-axis at the point (0, -5). From that point, it rises 3 units vertically for every 2 units it moves horizontally to the right. Write the equation of this line in slope-intercept form.
Solution:
The slope-intercept form of a line is: y = mx + c
where: m is the slope, c is the y-intercept.
The line crosses the y-axis at (0, -5), so: c = -5
It rises 3 units for every 2 units moved to the right, so the
slope is: m = \(\frac{3}{2}\)
Substituting into the slope-intercept form:
y = \(\frac{3}{2}\)x – 5
Question 2.
Write the equation of a line in slope-intercept form that is parallel to the line y = 5x -12 and passes through the point (0, 9).
Solution:
Parallel lines have the same slope.
The given line is: y = 5x – 12
So, the slope is: m = 5
The required line passes through (0, 9), which means the y-intercept is: c = 9.
Using slope-intercept form:
y = mx + c
Substitute m = 5 and c = 9:
y = 5x + 9
Question 3.
Determine the equation of the line in slope-intercept form that is perpendicular to the line y = \(\frac{x}{3}\) + 4 and passes through the origin.
Solution:
The given line is: y = \(\frac{x}{3}\) + 4
So, its slope is: m = \(\frac{1}{3}\)
For perpendicular lines, the product of two lines is -1. Thus, the slope of the required line is the negative
reciprocal of \(\frac{1}{3}\) i.e., -3.
Since the line passes through the origin, its y-intercept is 0. Using slope-intercept form:
y = mx + c
y = -3x + 0
Therefore, the equation of the line is: y = -3x
Question 4.
A straight line passes through the points (0, -6) and (4, 10). Find the equation of this line in slope-intercept form.
Solution:
The slope-intercept form of a line is:
y = mx + c
Where, m is the slope and c is the y-intercept.
Find the slope, using the points (0, -6) and (4, 10):
m = \(\frac{10-(-6)}{4-0}\)
m = \(\frac{16}{4}\) = 4
Since the line passes through (0, -6), the y-intercept is:
c = -6
So, the equation of the line is:
y = 4x – 6
Question 5.
Convert the linear equation 8x – y + 7 = 0 into slope- intercept form.
Solution:
Given, equation of line is: 8x – y + 7 = 0
To convert it into slope-intercept form y = mx + c, solve
for y.
8x + 7 = y
So, y = 8x + 7
Here, the slope is 8 and the y-intercept is 7.