Slope Intercept Form of a Straight Line

Q.

Find the equation of a line whose: y-intercept = 2 and slope = 3.

Q. Solve the following system of equation graphically:
$$\begin{gathered} 2x-3y+13=0 \\ 3x-2y+12=0 \end{gathered}$$

Q.

Find the equation of a line that has $y$-intercept as $4$ and is perpendicular to line joining $(2,-3)$ and $(4,2)$.

Q.

Draw the graph of the equation $2x+3y=12$ At what point does the graph of the equation cuts the $x$ axis and $y$ axis?

Q. Draw the graphs representing the equations 4x +3y=24 and 3y=4x + 24 on the same graph paper . Write the Co-ordinate of the point of intersection of these and find the area of the triangle formed by these lines and the X-axis.

Q. For equation x = a, the graph will be?

1. Parallel to x-axis
2. Parallel to y-axis
3. Remain at the origin
4. None of the above

Q.

What will be the value of m and $c$ if the straight line $y=mx+c$ passes through the points $(3,-4)$ and $(-1,2)$?

Q.

Assertion: All the points (1, 0), (-1, 0), (2, 0) and (5, 0) lie on the x – axis.
Reason: Equation of the x-axis is y = 0

Choose the correct option.

1. Both assertion and reason are correct and reason is the correct explanation of assertion.
2. Both assertion and reason are correct, but reason is not the correct explanation of assertion.
3. Assertion is correct but reason is incorrect.
4. Assertion is incorrect but reason is correct.

Q.

A motorcyclist is moving along the line $x-y=2$and another motorcyclist is moving along the line $x-y=4.$ Find out their moving direction.

Q. Solve the following system of equation graphically:
$$\begin{gathered} 2x+3y+5=0 \\ 3x-2y-12=0 \end{gathered}$$

Q. Equation of a line with slope 5 and y-intercept -8 is ______

1. $y=5x-8$
2. $y=5x+8$
3. $y=8x-5$
4. $y=8x+5$

Q. Find the slope of a line perpendicular to a line x+2y+1 = 0.

Q.

Find the equation of the straight line that has y - intercept 5 and is parallel to the straight line x - 3y = 3

1. 3x - y + 5 = 0

2. x - y +5=0

3. x - 3y + 15 =0

4. 2x - 3y +12 = 0

Q.

ABCD is a parallelogram where A(x, y), B(5, 8), C(4, 7) and D(2, -4). Find :

(i) co-ordinates of A

(ii) equation of diagonal BD.

Q.

Find the equation of a line with y – intercept = 5 & passing through the point (–4, 7).

1. – y = 5

2. – 2y = 5

3. + 2y = 10

4. - + 2y = 5

5. 2 + 2y = 5

Q.

Find the equation of a line whose: y-intercept = -1 and inclination = ${45}^{\circ }$.

Q.

Write the equation of line parallel to $x-$axis and distance $6$ unit from below the $x-$axis.

Q.

The line through P(5, 3) intersects y-axis at Q.

(i) Write the slope of the line.

(ii) Write the equation of the line.

(iii) Find the co-ordinates of Q.

Q.

If the line x - 4y - 6 = 0 is the perpendicular bisector of the line segment PQ and the coordinates of P are (1, 3), find the coordinates of Q.

Q.

If the x-intercept and y-intercept of a straight line are 3/2 and 4/3 respectively, then find the equation of the straight line.

1. 8x + 6y = 12

2. 8x + 9y = 14

3. 4x + 9y = 12

4. 8x + 9y = 12

Q. The pair of equations x = a and y = b graphically represents lines which are

(a) parallel
(b) coincident
(c) intersecting at (a, b)
(d) intersecting at (b, a)

Q.

The equation of a line is x - y = 4. Find its slope and y-intercept. Also, find its inclination.

Q.

If the straight lines $3x-5y=7and4x+ay+9=0$are perpendicular to one another , find the value of $a$.

Q.

Equation of a line parallel to the x-axis and at a distance ${}^{\prime }{p}^{\prime }$ from it, is ____________ .

1. x - p = 0

2. y - p = 0

3. y = 0

4. x = p

Q.

If the line y = mx + 8 contains the point (-4, 4), calculate the value of m.

1. -1

2. 1

3. 2

4. -2

Q. If a curve cuts the x-axis at three points, then it has _____ zeros.

1. 1
2. 2
3. 3
4. 4

Q.

Find the equation of a line whose slope is $-1$ and y-intercept is 5.

1. $x+y=4$

2. $x+y=5$

3. $x+y=2$

4. $x+y=3$

Q.

The equation of sides rectangle ABCD are given as follows:

Equation of AB: = –2, equation of BC: = 2, equation of CD: = 6, equation of AD: = –1. Find the coordinates of A, B, C, D. Hence find the equation of the diagonal AC.

1. 3x – 8y + 2 = 0

2. 8x – 3y + 5 = 0

3. 2x – 3y + 8 = 0

4. 8x – 3y + 2 = 0

Q.

If the x-intercept and y-intercept of a straight line are $\frac{3}{2}$ and $\frac{4}{3}$ respectively, then find the equation of the straight line.

1. 4x + 9y = 12

2. 8x + 9y = 12

3. 8x + 6y = 12

4. 8x + 9y = 14

Q. The graph of the linear equation $2x+3y=6$ intersects the $y-$axis at the point

1. $(2,0)$
2. $(3,0)$
3. $(0,3)$
4. $(0,2)$