Question

Write the equation of the line that passes through (3, 4) and (2, −1) in slope-intercept form.

a
y = 3x − 7

b
y = 3x − 5

c
y = 5x − 11

d
y = 5x − 9

Answer 1

Option C

y=5x-11

Explanation:

We first find the gradient,m, of the line that passes through the points (3,4) and (2,-1)

Let

x=3

y=4

`x_1=2`

`y_1=-1`

`m=(y - y_1)/(x - x_1)`

By substitution,

`m=(4-(-1))/(3-2)=(4 + 1)/(1) = (5)/(1)=5`

Putting that m=5, x=3 and y=4 into the general equation,

y=mx+c

This implies that

4=5(3)+c

4=15+c

4-15=c

c=-11

The equation of the line is given as

y=mx+c

where m=5 and c=-11

Hence y=5x-11