Question

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

Answer 1

Answer:

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

Step-by-step 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):

$\sf{}m = \frac{x- x_1}{y - y_1} = \frac{y_2 - y_1}{x_2 - x_1} \\ \\ \sf{}m = \frac{y_2 - y_1}{x_2 - x_1}$

$\sf{}m = \frac{8 - 4}{5 - 3} = \cancel \frac{4}{2} = 2$

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 $\underline\mathfrak\red{{{y = 2x + 2}}}$