Write the equation of the line that contains the indicated pair of points. Express the final equation in standard form.
(−3, 1) and (9, −3)
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To find the equation of a line passing through two given points, you can use the formula for the slope-intercept form of a line, which is:
y = mx + b
where m represents the slope of the line, and b represents the y-intercept.
Step 1: Calculate the slope (m) using the given points.
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (-3, 1) and (9, -3), we substitute the values into the formula:
m = (-3 - 1) / (9 - (-3))
m = -4 / 12
m = -1/3
Step 2: Substitute the slope (m) and one of the points (x, y) into the slope-intercept form equation.
Using the point (-3, 1), substitute the values into the equation y = mx + b:
1 = (-1/3)(-3) + b
Simplifying the equation:
1 = 1 + b
Step 3: Solve for the y-intercept (b).
To find the value of b, subtract 1 from both sides of the equation:
b = 1 - 1
b = 0
Step 4: Rewrite the equation in standard form.
Starting with the slope-intercept form equation, y = mx + b, substitute the values of m and b:
y = (-1/3)x + 0
Since the term "-1/3" is the coefficient of x, and "0" is the constant term, you can multiply the entire equation by 3 to eliminate the fraction:
3y = -x + 0
Simplifying further, you get:
x + 3y = 0
Therefore, the equation of the line passing through the points (-3, 1) and (9, -3) in standard form is:
x + 3y = 0