Slope is defined as rise over run, which can be expressed as the difference of the y-coordinates divided by the difference of the x-coordinates. If we rise, we are moving vertically, or along the y-axis. If we run, we are moving horizontally, or along the x-axis.

The formula for the slope m of a line given two points (x1, y1) and (x2, y2) that lie on the line is:

m = (y2 - y1)/(x2 - x1)

m = (15 - 5)/(-6 - 4)

m= 10/-10

m = -1

Now, we can use the slope-intercept form of the equation of a line to obtain the equation of the line that satisfies the conditions outlined in the problem. Slope-intercept form is:

y = mx + b

Again, m represents the slope, while b stands for the y-intercept. We can use either point on the line to represent x and y. Let's choose the point (4, 5)

5 = -1(4) + b

5 = -4 + b

9 = b

The equation of the line is:

y = -x + 9

7 0

3 years ago

The graph of F(x) shown below resembles the graph of G(x) = x ^ 2 but it has been changed somewhat . Which of the following coul

sukhopar [10]

Answer:

f(x) = 3 $x^{2}$ + 2

Step-by-step explanation:

Given G(x) = $x^{2}$

As we can see, the graph of f(x) is 2 units above the graphof g(x) in vertical (vertical shift)

=> f(x) = a $x^{2}$ + 2

As you can see, the graph of f(x) is stretched vertically by a dilation factor of 3

and there is no reflection, so a= 3

=> the equation of f(x) is: f(x) = 3 $x^{2}$ + 2

5 0

3 years ago