Question

Determine the equation of the line thatpasses through (0, 2) and (4, 5). Put inslope-intercept form.

Answer 1

Given:

Point ( 0, 2) and (4, 5)

The coordinates are:

x₁=0 y₁=2 x₂=4 y₂=5

First, we need to find the slope(m) using the formula below:

`\text{slope(m)}=(y_2-y_1)/(x_2-x_1)`

Substitute the values and evaluate.

`\text{slope(m)}=(5-2)/(4-0)=(3)/(4)`

Next, is to find the intercept(b) by substituting m=3/4 x=0 and y=2 into y=mx+b and then solve for b.

2 = 3/4 (0) + b

b=2

We can now proceed to form the equation by substituting the values of m and b into y=mx + b.

Hence, the equation of the line is:

`y=(3)/(4)x\text{ + 2}`