The correct answer is y = -2x + 16. In slope-intercept form, the formula is y = mx + b, where m is the slope and b is the y-intercept, or the place where the line crosses the y-axis. For this line, the y-intercept is positive 16, because the line crosses the y-axis at 16. Therefore, we know that the equation is y = mx + 16. Now, we just need to find the slope. By counting squares, we can see that the line goes down 4 and right 2. You can check this by taking two points on the line and subtracting them. For instance, the line goes from y 16 to y 12, which has a 4 unit difference. Therefore, the line goes down 4. It goes from x 0 to x 2, meaning that there is a difference of 2 between them, and, since the line is going right, the 2 is positive. Since slope = y/x, the slope is -4/2, or -2. Therefore, the slope is -2.
Adding all this together, the slope in slope-intercept form is y = -2x + 16.
It's y=-2x + 16 because the graph starts at 16 and goes down 2 and over 2. The y-intecept is 16 and thats the only equation that has that as the y=intercept
From the given information, the parabola is a sideways parabola facing left with vertex at the origin. Required equation is (y - 0)^2 = 4p(x - 0) y^2 = 4px
But 0 + p = -8 => p = -8
Therefore, required equation is y^2 = 4(-8)x y^2 = -32x
The transformations that can occur to the graph of the function y = cos x that will exhibit changes would be changes to the angle, or changes to the coefficient. The transformations can be viewed as follows:
y = cos x transforms to y = cos (kx)
k > 1 ; a horizontal shrink occurs 0 < k < 1 ; a horizontal stretch occurs
y = cos x transforms to y = A cos x
|A| > 1 ; a vertical stretch occurs |A| < 1 ; a vertical shrink occurs
