Final answer:
The point-slope form of the equation is y - 4 = -x + 1. The slope-intercept form is y = -x + 5. The standard form is x + y - 5 = 0.
Step-by-step explanation:
Point-slope:
The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using the given points (1,4) and (6, -1):
Slope (m) = (y2 - y1) / (x2 - x1) = (-1 - 4) / (6 - 1) = -5 / 5 = -1
Using the point-slope form:
y - 4 = -1(x - 1)
y - 4 = -x + 1
Slope-intercept:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Using the slope we calculated (-1) and one of the given points (1,4):
4 = -1(1) + b
b = 5
Therefore, the equation in slope-intercept form is y = -x + 5.
Standard form:
The standard form of a linear equation is Ax + By = C, where A, B, and C are constants, and A, B are not both zero.
We can convert the equation from slope-intercept form to standard form:
y = -x + 5
x + y = 5
x + y - 5 = 0