A line passes through the points (4,-8) and (6,-9) write its equation in slope intercept form
To find the equation of a line in slope-intercept form, we need to determine the slope of the line and the y-intercept.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the points (4, -8) and (6, -9), we can substitute these coordinates into the formula to find the slope:
m = (-9 - (-8)) / (6 - 4)
m = (-9 + 8) / 2
m = -1 / 2
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is given by:
y - y₁ = m(x - x₁)
Using the point (4, -8) and the slope -1/2, we can now substitute these values into the equation:
y - (-8) = -1/2(x - 4)
y + 8 = -1/2(x - 4)
Now, let's simplify this equation and rewrite it in slope-intercept form y = mx + b:
y + 8 = -1/2x + 2
y = -1/2x + 2 - 8
y = -1/2x - 6
Therefore, the equation of the line passing through (4, -8) and (6, -9) in slope-intercept form is y = -1/2x - 6.