(6, 1) and (5, 4)
a) Using variables, write out the formula for the standard form of the equation.
b) Determine the slope of the line.
c) Write the point-slope form of the line.
d) Using the properties of algebra, rearrange the equation into the standard form.
a) The formula for the standard form of the equation is Ax + By = C, where A, B, and C are constants.
b) To determine the slope of the line, we can use the formula:
slope = (y2 - y1) / (x2 - x1)
Using the points (6, 1) and (5, 4), we have:
slope = (4 - 1) / (5 - 6) = 3 / -1 = -3
Therefore, the slope of the line is -3.
c) The point-slope form of the line is given by:
y - y1 = m(x - x1)
Using the point (5, 4) and the slope -3, we have:
y - 4 = -3(x - 5)
d) Rearranging the equation:
y - 4 = -3x + 15
y = -3x + 19
The equation is now in slope-intercept form. Let's rearrange it into the standard form:
3x + y = 19
So, the standard form of the equation is 3x + y = 19.