Consider the graph of the function
f (x) = x2 − x − 30
.
(a) Find the equation of the secant line joining the points (−4, −10), and (6,0).
To find the equation of the secant line joining the points (-4, -10) and (6, 0) on the graph of the function f(x) = x^2 - x - 30, we need to find the slope of the secant line and then use the point-slope form of a linear equation.
Step 1: Find the slope of the secant line.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Using the given points (-4, -10) and (6, 0):
slope = (0 - (-10)) / (6 - (-4))
= 10 / 10
= 1
Step 2: Use the point-slope form of a linear equation.
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
Using the slope (m = 1) and either of the given points, say (-4, -10):
y - (-10) = 1(x - (-4))
y + 10 = x + 4
y = x - 6
Therefore, the equation of the secant line joining the points (-4, -10) and (6, 0) is y = x - 6.
To find the equation of the secant line joining the points (-4,-10) and (6,0) on the graph of the function f(x) = x^2 - x - 30, we need to find the slope of the secant line.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the points are (-4, -10) and (6, 0). So, plugging in the values into the formula, we have:
slope = (0 - (-10)) / (6 - (-4))
= (0 + 10) / (6 + 4)
= 10 / 10
= 1
The slope of the secant line is 1.
Now, we can use the point-slope form of a linear equation to find the equation of the secant line. The point-slope form is given by:
y - y1 = m(x - x1)
Using the point (-4, -10) and the slope 1, we have:
y - (-10) = 1(x - (-4))
y + 10 = x + 4
Simplifying, we get:
y = x - 6
So, the equation of the secant line joining the points (-4, -10) and (6, 0) is y = x - 6.
the slope of the line is (0+10)/(6+4) = 1
So, now use the point-slope form of the line. Pick either point, and you get
y+10 = 1(x+4)
or y+0 = 1(x+6)
either way you get y=x+6
Note that the function mentioned is irrelevant. You just need the two points.