To find the equation of the line, we first need to find the slope (m) of the line using the two given points. The slope (m) formula is:
m = (y2 - y1) / (x2 - x1)
Let's substitute the coordinates of the given points:
m = (-1 - 20) / (6 - (-3))
m = (-21) / (6 + 3)
m = -21 / 9
m = -7/3
Now that we have the slope (m), we can use the slope-intercept form (y = mx + b) and substitute the slope and one of the given points (-3, 20) to solve for the y-intercept (b):
20 = (-7/3)(-3) + b
Now simplify:
20 = 7 + b
20 - 7 = b
13 = b
So the value of b is 13.
Therefore, the equation of the line is:
y = (-7/3)x + 13
If the slope of a line and a point on the line are known, the equation of the line can be found using the slope-intercept form, y= mx + b. To do so, substitute the value of the slope and the values of x and y using the coordinates of the given point, then determine the value of b.
Using the above technique, find the equation of the line containing the points (- 3,20) and (6, - 1).
The equation of the line is
(Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)
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