Write an equation in slope-intercept form that satisfies the information given about the line
Goes through the points (6, 1) and (10, -1)
To write the equation of the line in slope-intercept form (y = mx + b), we first need to find the slope (m) and the y-intercept (b).
The slope (m) can be found using the formula:
m = (y₂ - y₁) / (x₂ - x₁),
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two given points.
Using the points (6, 1) and (10, -1), we have:
m = (-1 - 1) / (10 - 6).
m = (-2) / (4).
m = -1/2.
Now that we have the slope (m), we can substitute it into the equation y = mx + b, along with one of the points to find the y-intercept (b).
Using the point (6, 1):
1 = (-1/2)(6) + b.
1 = -3 + b.
b = 4.
Therefore, the equation of the line in slope-intercept form that satisfies the given information is:
y = (-1/2)x + 4.