Find the equation of the line shown

Question

asked Jul 27, 2021 114k views

2 Answers

Mahmoud Samir · Answer 1 · 2021-07-27T08:26:45+0000

The equation of the line passing through the given points is y =
$(1)/(2)x \)$ .

To find the equation of the line passing through the given points, we can use the slope-intercept form of a linear equation:

$y = mx + b$

where m is the slope and b is the y-intercept.

First, calculate the slope m using two of the given points, for example, (2,1) and (10,5):

$m = \frac{{\text{{change in }} y}}{{\text{{change in }} x}}$

$m = \frac{{5 - 1}}{{10 - 2}} = (4)/(8) = (1)/(2)$

Now that we have the slope
$($ (1)/(2) $)$ , we can use it in the slope-intercept form and substitute one of the points to find the y-intercept b.

Let's use the point (2,1):

$1 = (1)/(2)(2) + b$

Solve for b:

$1 = 1 + b$

$b = 0$

Now we have the slope
$($ (1)/(2) $)$ and the y-intercept 0, so the equation of the line is:

$y = (1)/(2)x$

Therefore, the equation of the line passing through the given points is y =
$(1)/(2)x \)$ .