Find the slope and y -intercept of the line x 3 + y 4 = 1 .

We are given to find the slope and y -intercept of the line x 3 + y 4 = 1 . We know that the equation of a straight line in the slope-intercept form is given by y = m x + c , where m is the slope and c is the y -intercept. We shall convert the given equation in the slope-intercept form and compare it with y = m x + c and obtain the values of m and c . Thus, we have, x 3 + y 4 = 1 ⇒ x 3 × 4 + y 4 × 4 = 1 × 4 ⇒ 4 3 x + y = 4 y = - 4 3 x + 4 Comparing this equation with y = m x + c , we obtain, m = - 4 3 and c = 4 . Therefore, the required slope is - 4 3 and y -intercept is 4 .

Find the value of p , given that the line y 2 = x - p passes through the point ( - 4 , 4 ) .

Given, y 2 = x - p ⇒ y = 2 x – 2 p Since, line pass through - 4 , 4 . Thus, we substitute x = - 4 and y = 4 in the given equation. ∴ 4 = 2 - 4 – 2 p ⇒ 4 + 8 = - 2 p ⇒ 12 = - 2 p ⇒ p = - 6 Hence, p = - 6

Given that a , 2 a lies on the line y 2 = 3 x - 6 find the value of a .

Given, a , 2 a lies on the line y 2 = 3 x - 6 . Substituting x = a and y = 2 a in the given equation, we get, 2 a 2 = 3 a - 6 ⇒ a = 3 a - 6 ⇒ a - 3 a = - 6 ⇒ - 2 a = - 6 ⇒ a = - 6 - 2 ⇒ a = 3 Hence, the value of a is 3 .

E M B I B E

Understanding ICSE Mathematics Class 10>Chapter 12 - Equations of a Straight Line>Exercise 12.1>Q 7

MEDIUM

10th ICSE

IMPORTANT

Earn 100

Find the slope and $y$ -intercept of the line $x - 2 y - 1 = 0$ .

Important Questions on Equations of a Straight Line

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 12 - Equations of a Straight Line>Exercise 12.1>Q 7

Find the slope and

y

-intercept of the line

4 x - 5 y - 9 = 0

.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 12 - Equations of a Straight Line>Exercise 12.1>Q 7

Find the slope and

y

-intercept of the line

3 x + 5 y + 7 = 0

.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 12 - Equations of a Straight Line>Exercise 12.1>Q 7

Find the slope and

y

-intercept of the line

\frac{x}{3} + \frac{y}{4} = 1

.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 12 - Equations of a Straight Line>Exercise 12.1>Q 7

Find the slope and

y

-intercept of the line

y - 3 = 0

.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 12 - Equations of a Straight Line>Exercise 12.1>Q 7

Find the slope and

y

-intercept of the line

x - 3 = 0

.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 12 - Equations of a Straight Line>Exercise 12.1>Q 9

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The given figure represents the lines $y = x + 1$ and $y = \sqrt{3} x - 1$ . Write down the angles that the lines make with the positive direction of $x ‐$ axis. Hence, determine the angle $θ$ .