Question

A line passes through the point (1, –3) and has a slope of 3 . Which point is on the same line?


Question 10 options:

A. (–9, –5)


B. (1, -6)


C. (0, –6)


D. (, 13)

Answer 1

Answer:

what samjahay ne mahdshhshd

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

A line passes through the point (1, –3) and has a slope of 3.

We know,

Slope point form of a line

The equation of line which passes through the point (a, b) and having slope m is given by

$\red{\boxed{ \bf{ \: y - b = m(x - a)}}}$

So,

Here,

a = 1

b = - 3

m = 3

So, on substituting the values, we get

$\rm :\longmapsto\:y - ( - 3) = 3(x - 1)$

$\rm :\longmapsto\:y + 3 = 3x - 3$

$\rm :\longmapsto\:3x - y - 3 - 3 = 0$

$\rm :\longmapsto\:3x - y - 6= 0$

$\rm :\longmapsto\:3x - y = 6$

Now, to check whether the given points lie on the line or not, Let plot the line on graph paper.

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:3(0) - y = 6$

$\rm :\longmapsto\: - y = 6$

$\rm :\longmapsto\: y = - 6$

Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:3x - 0 = 6$

$\rm :\longmapsto\:3x = 6$

$\rm :\longmapsto\:x = 2$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 6 \\ \\ \sf 2 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , - 6) & (2 , 0)

➢ See the attachment graph.

Now, The points are given as

A. (–9, –5)

B. (1, -6)

C. (0, –6)

D. (1, 3)

From graph, we concluded that C ( 0, - 6 ) lies on the line.