Write an equation for the line that passes through the points (4,8) and (6,2).
the slope is (2-8)/(6-4) = -3
so the equation is
y-8 = -3(x-4)
To find the equation for the line that passes through the points (4,8) and (6,2), we need to determine the slope of the line. The slope (m) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the values from the given points, we have:
m = (2 - 8) / (6 - 4)
m = -6 / 2
m = -3
Now that we have the slope of the line, we can use the point-slope form of the equation:
y - y₁ = m(x - x₁)
We can select one of the given points, let's use (4,8) as (x₁, y₁):
y - 8 = -3(x - 4)
Simplifying further:
y - 8 = -3x + 12
Now we can rearrange the equation to slope-intercept form (y = mx + b) by isolating y:
y = -3x + 20
Therefore, the equation for the line that passes through the points (4,8) and (6,2) is y = -3x + 20.
To write the equation for the line that passes through two points, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1),
where (x1, y1) are the coordinates of one of the points on the line, and m is the slope of the line.
Let's find the slope first using the formula:
m = (y2 - y1) / (x2 - x1).
Using the coordinates (4, 8) and (6, 2), we have:
m = (2 - 8) / (6 - 4) = -6 / 2 = -3.
Now, pick one of the points and substitute its coordinates into the point-slope equation. Let's use (4, 8):
y - 8 = -3(x - 4).
Simplifying this equation, we get:
y - 8 = -3x + 12.
To express the equation in slope-intercept form (y = mx + b), rearrange the equation:
y = -3x + 12 + 8,
y = -3x + 20.
Therefore, the equation for the line passing through the points (4,8) and (6,2) is y = -3x + 20.