The graph of linear function g passes through the points and , as shown.
a.3c q3
What are the slope and y-intercept of the graph of g?
Question 3 options:
The slope is
, and the y-intercept is -1
The slope is
, and the y-intercept is -1
The slope is
, and the y-intercept is 1
The slope is
, and the y-intercept is 1
The slope of the linear function g can be determined by finding the change in y divided by the change in x between the two points. In this case, the change in y is -1 - 4 = -5 and the change in x is 2 - (-1) = 3. So the slope is -5/3.
The y-intercept can be found by looking at the y-coordinate when x = 0. From the graph, we can see that the y-intercept is -1.
Therefore, the correct answer is: The slope is -5/3 and the y-intercept is -1.
To find the slope of the linear function g, we can use the formula:
slope = (change in y)/(change in x)
Using the points given, we can calculate the slope as follows:
slope = (y2-y1)/(x2-x1)
Let's plug in the values:
Given point 1: (5, 2)
Given point 2: (1, 6)
slope = (6-2)/(1-5)
= (4)/(-4)
= -1
Therefore, the slope of the graph of g is -1.
Now let's find the y-intercept. The y-intercept is the value of y when x equals 0. From the graph, we can see that the y-intercept is -1.
Therefore, the slope of the graph of g is -1 and the y-intercept is -1.
The correct option is: The slope is -1, and the y-intercept is -1.
To find the slope and y-intercept of a linear function, you can use the formula for the slope-intercept form of a line, which is y = mx + b. In this formula, m represents the slope of the line, and b represents the y-intercept.
To determine the slope, you need to calculate the change in y divided by the change in x between any two points on the line. In this case, you can use the given points (3, 2) and (7, -2).
The change in y is -2 - 2 = -4, and the change in x is 7 - 3 = 4. Therefore, the slope is -4/4 = -1.
Next, to find the y-intercept, you can substitute the x and y values from one of the given points into the slope-intercept form of the line and solve for b. Let's use the point (3, 2):
2 = -1(3) + b
Simplifying this equation gives:
2 = -3 + b
Adding 3 to both sides:
2 + 3 = b
5 = b
Therefore, the y-intercept is 5.
So, the slope is -1 and the y-intercept is 5.
Looking at the given options, we can see that none of them match the correct answer.