Write an equation in standard form of the line that passes through the given points (2,6)(3,8)
-2x+y=2
thanks
To find the equation in standard form that passes through the given points, we first need to find the slope (m) of the line using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the given points (2,6) and (3,8):
m = (8 - 6) / (3 - 2) = 2 / 1 = 2
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation:
y - y₁ = m(x - x₁)
Using the point (2,6) and the slope (m = 2):
y - 6 = 2(x - 2)
Expanding the equation:
y - 6 = 2x - 4
Rearranging the equation to standard form:
2x - y = 2 - 6
Simplifying:
2x - y = -4
So, the equation in standard form that passes through the given points is:
2x - y = -4
To find the equation of the line that passes through two given points, you can use the point-slope form or slope-intercept form.
1. Using the point-slope form:
The point-slope form is given by:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one of the given points, and m is the slope of the line.
First, determine the slope:
m = (y2 - y1) / (x2 - x1)
Substituting the given coordinates (2,6) and (3,8):
m = (8 - 6) / (3 - 2)
m = 2 / 1
m = 2
Now, choose either one of the given points and substitute it into the equation along with the slope:
Using (2,6):
y - 6 = 2(x - 2)
y - 6 = 2x - 4
y = 2x - 4 + 6
y = 2x + 2
The equation of the line in point-slope form is y = 2x + 2.
2. Converting to standard form:
To convert the equation from point-slope form to standard form (Ax + By = C), rearrange the equation:
y = 2x + 2
-2x + y = 2
The equation in standard form is -2x + y = 2.