Write the standard form of the line that passes through the given points. Include your work for each step in your final answer. Type your answer in the box provided to submit your solution.
(7, -3) and (4, -8)
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)
Given the points (7, -3) and (4, -8), we can substitute the values into the formula:
slope = (-8 - (-3)) / (4 - 7)
slope = (-8 + 3) / (4 - 7)
slope = -5 / -3
Simplifying the fraction, we get:
slope = 5/3
c) The point-slope form of the line is given by:
y - y1 = m(x - x1)
Using the point (7, -3) as (x1, y1) and the slope we just calculated:
y - (-3) = (5/3)(x - 7)
y + 3 = 5/3(x - 7)
d) To rearrange the equation into the standard form, we distribute the slope:
y + 3 = (5/3)x - (5/3)(7)
y + 3 = (5/3)x - 35/3
Next, we bring all terms to one side of the equation:
(5/3)x - y = 35/3 - 3
To simplify the right side, we find a common denominator:
(5/3)x - y = 35/3 - 9/3
(5/3)x - y = 26/3
Finally, we can multiply through by 3 to get rid of the fraction coefficients:
3[(5/3)x - y] = 3(26/3)
5x - 3y = 26
Therefore, the standard form of the equation is 5x - 3y = 26.