(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.

1 answer

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.
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