Slope Intercept Form of a Line

Q.

The equations of the lines which pass through the point $\left(3,-2\right)$ and are inclined at $60°$ to the line $\sqrt{3}x+y=1$ are

1. $y+2=0,\sqrt{3}x-y-2-3\sqrt{3}=0$

2. $x-2=0,\sqrt{3}x-y+2+3\sqrt{3}=0$

3. $\sqrt{3}x-y-2-3\sqrt{3}=0$

4. None of the above

Q.

Find the equation of a line making an angle of ${150}^{\circ }$ with the x-axis and cutting off an intercept 2 from y-axis.

Q. The equation of the line whose slope is 3 and which cuts off an intercept 3 from the positive x - axis is

1. y=3x+9
2. None of these
3. y=3x-9
4. y=3x+3

Q.

Find the equations of the straight lines which pass through (4, 3) and are respectively parallel and perpendicular to the x-axis.

Q.

Find the equation of the line passing through $(2,2\sqrt{3})$ and inclined with x-axis at an angle of ${75}^{\circ }.$

Q.

If a line makes angles of $30°$ and $45°$ with x-axis and y-axis, then the angle made by it with z-axis is

1. $45°$

2. $60°$

3. $120°$

4. None of these

Q. Find graphically, the maximum value of Z = 2x + 5y, subject to constraints given below:

2x + 4y ≤ 8

3x + y ≤ 6

x + y ≤ 4

x ≥ 0, y ≥ 0 [CBSE 2015]

Q.

At which point the line $\frac{x}{a}+\frac{y}{b}=1,$ touches the curve $y=b{e}^{-\frac{x}{a}}$

1. $\left(0,0\right)$

2. $\left(0,a\right)$

3. $\left(0,b\right)$

4. $\left(b,0\right)$

Q.

Find the equation of a line that has y-intercept-4 and is parallel to the line joining (2, -5) and (1, 2).

Q.

The line parallel to the $X$-axis and passing through the point of intersection of the line $ax+2by+3b=0$ and $bx-2ay-3a=0$, where $(a,b)\ne (0,0)$, is

1. Above the$X-$axis at a distance of$\frac{3}{2}$

2. Above the$X-$-axis at a distance of $\frac{2}{3}$

3. Below the $X-$axis at a distance of $\frac{2}{3}$

4. Below the$X-$axis at a distance of $\frac{3}{2}$

Q.

Find the equation of the line parallel to x-axis and having intercept -2 on y-axis.

Q.

The area of the triangle bounded by the straight line $\mathrm{ax}+\mathrm{by}+\mathrm{c}=0$, $\left(a,b,c\ne 0\right)$ and the coordinate axes is equal to:

1. $\frac{1}{2}\left|\frac{{\mathrm{c}}^2}{\mathrm{ab}}\right|$

2. $\frac{1}{2}\left|\frac{{\mathrm{a}}^2}{\mathrm{ab}}\right|$

3. $\frac{1}{2}\left|\frac{{\mathrm{b}}^2}{\mathrm{ab}}\right|$

4. $1$

Q. The angle(s) formed by the positive $y-$axis and the tangent to $y=x^2+4x-17$ at $(\frac{5}{2},\frac{-3}{4})$ is(are)

1. ${\tan }^{-1}\left(9\right)$
2. $\frac{\pi }{2}-{\tan }^{-1}\left(9\right)$
3. $\frac{\pi }{2}+{\tan }^{-1}\left(9\right)$
4. $\pi -{\tan }^{-1}\left(9\right)$

Q.

Find the equation of the line which intercepts a length 2 on the positive direction of the x-axis and is inclined at an angle of ${135}^{\circ }$ with the positive direction of y-axis.

Q.

Find the equations of the bisectors of the angles between the coordinate axes.

Q. The equation of the line parallel to the line joining $(4,2)$ and $(2,4)$ and whose $y$-intercept is $4$ units along positive $y$- axis is

1. $y+x+4=0$
2. $x-y+4=0$
3. $2x+y=0$
4. $y+x-4=0$

Q.

Find the equation of the straight line intersecting y-axis at a distance of 2 units above the origin and making an angle of ${30}^{\circ }$ with the positive direction of the x-axis.

Q. The slope intercept form of the line $\frac{x}{2}+\frac{y}{4}=1$ is

1. $y=-2x+4$
2. $y=2x+4$
3. $y=4x+2$
4. $y=-4x+2$

Q.

What is Tangential?

Q.

Two lines passing through the point (2, 3) intersects each other at an angle of 60°. If slope of one line is 2, find equation of the other line.

Q.

What are the three methods used to graph a linear equation?

Q.

The perpendicular from the origin to a line meets it at the point (– 2, 9), find the equation of the line.

Q. The equation of a straight line(s) passing through $(1,2)$ and having intercept of length $3$ units between the straight lines $3x+4y=24$ and $3x+4y=12$, is

1. $y=2$
2. $x=1$
3. $7x+24y+41=0$
4. $7x-24y+41=0$

Q.

Find the equations to the straight lines which pass through the origin and are inclined at an angle of ${75}^{\circ }$ to the straight line $x+y+\sqrt{3}(y-x)=a$.

Q.

Find the equation of a straight line:

(i) with slope 2 and y-intercept 3; (ii) with slope -1/3 and y-intercept -4.

(iii) with slope -2 and intersecting the x-axis at a distance of 3 units to the left of origin.

Q. The equation(s) of the straight line passing through $(-2,-7)$ and having intercept length of $3$ units between the straight lines $4x+3y=12$ and $4x+3y=3$ is/are

1. $7x+24y+182=0$
2. $x+2=0$.
3. $y+7=0$
4. $24x+7y+97=0$

Q.

Find the equation of a line which makes an angle of $ta{n}^{-1}$ (3) with the x-axis and cuts off an intercept of 4 units on negative direction of y-axis.

Q. If the vertices of a triangle are $A(10,4),B(-4,9)$ and $C(-2,-1)$, then the equation of its altitudes are

1. $x-5y+10=0$
2. $12x+5y+3=0$
3. $14x+5y+23=0$
4. $14x-5y+23=0$

Q. The value of $\left[\right(\sqrt{3}+\sqrt{2}{)}^6]$ is
( Here, $[.]$ represents the greatest integer function )

Q.

Find the equation of the straight line which has y-intercept equal to $\frac{4}{3}$ and is perpendicular to $3x-4y+1=0.$