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.)
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