Slope of a Line

Q.

The differential equation of the family of straight lines whose slope is equal to y-intercept, is

1. $(\mathrm{x}+1)\frac{d\mathrm{y}}{d\mathrm{x}}–\mathrm{y}=0$

2. $(\mathrm{x}+1)\frac{d\mathrm{y}}{d\mathrm{x}}+\mathrm{y}=0$

3. $\frac{d\mathrm{y}}{d\mathrm{x}}=\frac{(\mathrm{x}-1)}{(\mathrm{y}-1)}$

4. $\frac{d\mathrm{y}}{d\mathrm{x}}=\frac{(\mathrm{x}+1)}{(\mathrm{y}+1)}$

Q.

The equations to a pair of opposite sides of a parallelogram are $x^2-5x+6=0$ and $y^2-6y+5=0$. The equations to its diagonals are

1. $x+4y=13$, $y=4x-7$

2. $4x+y=13$, $4y=x-7$

3. $4x+y=13$, $y=4x-7$

4. $y-4x=13$, $y+4x=7$

Q. If Y is directly proportional to X then:
(k is a constant)

1. $Y=kX$
2. $Y=\frac{k}{X}$
3. $Y=k+X$
4. $Y=k-X$

Q.

What is the $y$-intercept for the straight line $2x-3y=5$?

Q.

If the line
$(3x+14y+7)+k(5x+7y+6)=0$
is parallel to the y-axis, then the value of $k$ is

1. 1/3

2. −3/5

3. −2

4. 2

Q. Find the value of $x$ for the points $(x,-1)(2,1)(4,5)$ are collinear.

Q.

Find the slope and the $y$intercept made by the line $\frac{x}{1.5}+\frac{y}{0.5}=1$

Q.

The equation of a line AB is 2x - 2y + 3 = 0, its slope is ______.

1. $\frac{1}{2}$

2. 1

3. $\frac{3}{2}$

4. 2

Q.

Which of the following statement is / are correct for equation 2x - 3y + 5 = 0

1. Slope of the straight line is $\frac{2}{3}$

2. x-intercept of the straight line is $\frac{-5}{2}$

3. y-intercept of the straight line is $\frac{5}{3}$

1. All 1, 2 & 3

2. only 2&3

3. only 3&1

4. only 1 & 2

Q. The given table and the graph shows the amount of work done by workers P, Q, and R and the time taken. Which of the following workers shows a proportional relationship?

P
x: Time (in days)	$\frac{12}{15}$	$\frac{5}{2}$
y: Amount of work done	$\frac{1}{3}$	$\frac{2}{3}$

1. R and Q
   
2. P, Q, and R
   
3. R
4. P

Q.

Two sides of a rhombus are along the lines x-y+1=0 and 7x-y-5=0. If its diagonals intersect at (-1, -2), then which one of the following is a vertex of this rhombus?

1. $(-3,-9)$

2. $(\frac{1}{3},-\frac{8}{3})$

3. $(-3,-8)$

4. $(-\frac{10}{3},-\frac{7}{3})$