Draw the graph of the following equations, and identify their slopes and y-intercepts. Also, find the coordinates Class 9

Draw the graph of the following equations, and identify their slopes and y-intercepts. Also, find the coordinates Class 9

Question 1.

Draw the graph of the following equations, and identify their slopes and y-intercepts. Also, find the coordinates of the points where these lines cut the y-axis. Class 9

(i) y = -3x + 4

(ii) 2y = 4x + 7

(iii) 5y = 6x - 10

(iv) 3y = 6x - 11

Are any of the lines parallel?

Solution:

y = -3x + 4

Comparing with y = ax + b, we get

Slope (a) = 2

y-intercept (b) = 4

The line cuts the y-axis at (0, 4).

ii. 2y = 4x + 7

∴ y = 2x + $\frac{7}{2}$

Comparing with y = ax + b, we get Slope (a) = 2

y-intercept (b) = $\frac{7}{2}$ = 3.5

The line cuts the y-axis at (0, 3.5).

iii. 5y = 6x - 10

∴ y = $\frac{6}{5}$x - 2

Comparing with y = ax + b, we get Slope (a) = $\frac{6}{5}$

y-intercept (b) = -2

The line cuts the y-axis at (o, -2)

iv. 3y = 6x - 11

Dividing both sides by 3, we get

∴ y = 2x - $\frac{11}{3}$

Comparing with y = ax + b, we get Slope (a) = 2

y-intercept (b) = -$\frac{11}{3}$

The line cuts the y-axis at (o, -$\frac{11}{3}$)

Lines 2y = 4x + 7 but 3y = 6x - 11 have the same slope 2, but different y-intercepts.

∴ They are parallel to each other.