The slope of the line isand they-intercept is.

The equation of the line is.

This is the parent graph of. Since the graph in question is negative, then we flip the quadrants in which it will approach infinity. So the graph ofwill start in quadrant 2 and end in 4.

Plug inforto find a point on the line:

Thus,is a point on the line.

Plug inforto find a second point on the line:

is another point on the line.

Now we know that the line passes through the pointsand.

A quick sketch of the two points reveals that the line passes through all but the third quadrant.

In order to find the equation of a line in slope-intercept form, whereis the slope andis the y-intercept), one must know or otherwise figure out the slope of the line (its rate of change) and the point at which it intersects the y-axis. By looking at the graph, you can see that the line crosses the y-axis at. Therefore,.

Slope is the rate of change of a line, which can be calculated by figuring out the change in y divided by the change in x, using the formula

.

When looking at a graph, you can pick two points on a graph and substitute their x- and y-values into that equation. On this graph, it's easier to choose points likeand. Plug them into the equation, and you get

Plugging in those values forandin the equation, and you get

Answer: (1/2,0) and (0,-2)

Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equationis in slope-intercept () form, meaning that the y-intercept, b, is actually given in the equation. b = -2, which means that our y-intercept is -2. The ordered pair for expressing this is (0,-2)

Finding the x-intercept: To find the x-intercept of the equation, we must find the point where the line of the equation crosses the x-axis. In other words, we must find the point on the line where y is equal to 0, as it is when crossing the x-axis. Therefore, substitute 0 into the equation and solve for x:

The x-interecept is therefore (1/2,0).

The line in the diagram has a negative slope and a positive y-intercept. It has a negative slope because the line moves from the upper left to the lower right, and it has a positive y-intercept because the line intercepts the y-axis above zero.

The only answer choice with a negative slope and a positive y-intercept is

Using the distance formula, calculate the distance from each of these points to the origin, (0, 0). While each answer choice has coordinates that add up to seven, (-1, 8) is the coordinate pair that produces the largest distance, namely, or approximately 8.06.

The point向右平移5单位将沿着x-axis, meaning that you will add 5 to the original x-coordinate, so the new. The point shifted down by three units will shift down the y-axis, meaning that you will subtract three from the original y-coordinate, so the new.

The resultant coordinate is.

The point can be reached from the origin by moving 2 units right then 6 units up. This makes the first coordinate 2 and the second coordinate 6.

The graph is a down-opening parabola with a maximum of. Therefore, there are no y values greater than this for this function.