Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided to submit your solution.
(6, 1) and (5, 4)
To find the equation of the line that passes through the given points, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
First, let's find the slope (m) of the line using the two points (6, 1) and (5, 4):
m = (y2 - y1) / (x2 - x1)
= (4 - 1) / (5 - 6)
= 3 / (-1)
= -3
Now that we have the slope, we can choose one of the points (let's use the first point, (6, 1)) in the point-slope form:
y - 1 = -3(x - 6)
Let's simplify this equation:
y - 1 = -3x + 18
To write the equation in standard form (Ax + By = C), we move all terms to one side of the equation:
3x + y = 19
Therefore, the standard form of the line that passes through the points (6, 1) and (5, 4) is 3x + y = 19.