Question

What are the linear equations for the lines passing through the following points (3,4) and (5,8)

Answer 1

The equation of the line is y = 2x + 2

Explanation:

Given:

• The two points are (3, 4) and (5, 8)

To find:-

• Equation of a linear line

Solution:-

Equation of a linear line can be placed in the format:

• y = mx + c

Formula for finding the slope(m):

`\sf{}m = (x- x_1)/(y - y_1) = (y_2 - y_1)/(x_2 - x_1) \\ \\ \sf{}m = (y_2 - y_1)/(x_2 - x_1)`

`\sf{}m = (8 - 4)/(5 - 3) = \cancel (4)/(2) = 2`

Form the intermediate equation:

y = mx + c

`\mathtt{y = 2x + c}`

Find the y-intercept:

Substitute (3,4) into the equation

`: \longrightarrow \: \mathtt{y = 2x + c} \\ \\ : \longrightarrow \:\mathtt{4 = 2(3) + c} \\ \\ : \longrightarrow \: \mathtt{4 = 6 + c} \\ \\ : \longrightarrow \: \mathtt{c = 6 - 4} \\ \\ : \longrightarrow \: \mathtt{c = 2}`

Form the equation:

`: \longrightarrow \: \mathtt{y = 2x + c} \: \\ \\ \mathtt{putting \: values \: of \: c} \\ \\ : \longrightarrow \: \mathtt{y = 2x + 2}`

The equation of the line is
`\underline\mathfrak\red{{{y = 2x + 2}}}`