Slope of a Line

Q.

If $\lambda x^2-5xy+6y^2+x-3y=0$ represents a pair of straight lines, then their point of intersection is:

1. $\left(1,3\right)$

2. $\left(-1,-3\right)$

3. $\left(3,1\right)$

4. $\left(-3,-1\right)$

Q. The equation has a positive slope and a negative
y-intercept.

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

Q.

How do you interpret the slope and $y$-intercept $?$

Q.

Two students are reading a novel. Ashley reads$10$ pages per day. Carly reads $8$ pages per day , but she started early and is already on page $40$. Write a system of equations to represent the situation, using $d$ for days and $p$ for pages.

Q. The slope of the line $y=x$ is

1. 1
2. 2
3. 3

Q. The slope of the line: $2x+3y+1=0$ is

1. -2
2. $\frac{2}{3}$
3. $\frac{-2}{3}$

Q. The horizontal distance of the point from the $y-$axis is called run.

1. True
2. False

Q. The vertical distance of the point from the $x-$axis is called

1. Run
2. Rise
3. Slope

Q.

The table shows the lengths (in inches) of your hair months after your last haircut. The points in the table lie on a line. Find and interpret the slope of the line. After how many months is your hair $4inches$ long?

Q.

What is the slope formula for two points?

Q. Find the slope of the line $y=0$.

1. 1
2. 0
3. Not defined
4. 2

Q. What is the slope of the line shown?

Q. Three vertices of a parallelogram taken in order are $(-1,-6),(2,-5)$ and $(7,2).$ The fourth vertex is :

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

Q. Which of the following is the equation of given line joining point A and point B?

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

Q. The equation has a positive slope and a negative
y-intercept.

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

Q. The equation of a line can be determined if only the slope value is given.

1. True
2. False

Q. Complete the table and identify the equation for function B.


On observing, we see that function B has slope compared to slope of function A.

1. smaller
2. greater
3. same

Q. The graph of the line $y=mx+b$ is given by some random points. What is the slope and intercept of the line?

1. $m=-2,b=3$
2. $m=-2,b=3$
3. $m=-2,b=-3$
4. $m=2,b=-3$

Q. Which one of the following conclusions can be made for the given lines?

1. $\text{slope of line}A\text{= slope of line}B$
2. $\text{slope of line}A\text{> slope of line}B$
3. $\text{slope of line}B\text{> slope of line}A$
4. none of the above

Q. What would be the value of the slope of a line passing through the point $(4,3)$ and the origin $(0,0)$?

1. $\frac{4}{3}$
2. $\frac{3}{4}$
3. $\frac{1}{3}$
4. $\frac{1}{4}$

Q.

Check whether the pair of lines $x+3y-7=0$ and $3x-y-21=0$ is perpendicular or not.

Q. Which of the following graphs represents a proportional relationship between y and x, where the unit rate of change of y with respect to x is 2.5?

Q.

Show that the pair of the lines $3x-y=0$ and $x+3y-3=0$is perpendicular.

Q. In the figure above, if line $l$ has a slope of $-2$, what is the $y$-intercept of $l$?

1. $7$
2. $8$
3. $12$
4. $10$
5. $9$

Q. If $A(-2,1),B(1,0),C(x,3)$ and $D(1,y)$ are the vertices of parallelogram, then find the values of $x$ and $y$.

Q. If A increases correspondingly with increase in B, then A is said to be directly proportional to B.

1. True
2. False

Q. Select the correct option(s) for the line $3x-2y=2.$

1. slope $=\frac{3}{2}$
2. slope $=-\frac{3}{2}$
3. $y-$intercept $=1$
4. $y-$intercept $=-1$

Q. The slope of line 5y=10x+2 will be

Q. Which relation represents the Slope intercept form of a line?

1. $y=mx+b$
2. $x=my+b$
3. $b=xy+m$

Q. In an isosceles triangle, Sum of two equal angles is ${36}^0$ more than twice the value of third angle. Find the linear equation of above condition along with slope of equation of straight line obtained.

1. Slope$=2$
2. Slope$=1$
3. linear equation will be $y=x-18$, where $x$ is measure of identical angles and $y$ is third angle.
4. linear equation will be $3y=2x+36$, where $x$ is measure of identical angles and $y$ is third angle.