How can I find the linear equation of a line through points

[dancho]

How can I find the linear equation of a line through the points: (1, 2) and (7, 8) ?

[red_dog]

The equation of the line passing through the points [tex]M_1(x_1,y_1),M_2(x_2,y_2)[/tex] is

[tex]\displaystyle\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}[/tex]

[leesajohnson]

x−x1 / x2−x1 = y−y1 / y2−y1

[Guest]

Or: any (non-vertical) graph can be written y= ax+ b. If the graph goes through the point (1, 2) then when x= 1, y= 2 so 2= a+ b. If the graph goes through (7, then when x= 7, y= 8 so 8= 7a+ b. Solve the two equations a+ b= 2 and 7a+ b= 8 for a and b.

[Guest]

x−x1 / x2−x1 = y−y1 / y2−y1

No! This says [tex]x- \frac{x1}{x2}- x_1= y- \frac{y1}{y2}- y1[/tex] which is NOT what is intended! If you cannot use Latex, please use parenthese: (x- x1)/(x2- x1)= (y- y1)/(y2- y1).

[GeradHum]

To find the linear equation of a line that passes through two given points, such as (1, 2) and (7, 8), you can follow these steps:

Step 1: Calculate the slope (m) of the line using the formula:

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of the two given points.

Applying the values of the points (1, 2) and (7, 8) in the slope formula, we obtain:

m = (8 - 2) / (7 - 1) = 6 / 6 = 1

Therefore, the slope of the line is 1.

Step 2: Using the slope (m) and one of the given points (x1, y1), you can write the equation of the line in point-slope form:

y - y1 = m(x - x1)

Using the point (1, 2) and slope 1, we have:

y - 2 = 1(x - 1)

Simplifying the equation:

y - 2 = x - 1

Step 3: If you want the equation in general form (y = mx + b), you can solve for y:

y = x + 1

So, the linear equation of the line that passes through the points (1, 2) and (7, 8) is y = x + 1.

This equation represents a line with a positive slope of 1 and a y-intercept at the point (0, 1).

I hope this helps you find the linear equation of the line that passes through the given points. If you have any further questions, feel free to ask.