Look at the graph:
Graph: 0,5 3,3 6,1
a. What is the y-intercept:
b. What is the slope:
c. What is the equation of the line in slope-intercept form:
d. This is a ___(blank) relationship.
a. The y-intercept is the value of y when x is equal to 0. From the graph, the y-intercept is 5.
b. The slope is the change in y divided by the change in x. From the graph, the slope is (3-5)/(3-0) = -2/3.
c. The equation of the line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Substituting the values, the equation is y = (-2/3)x + 5.
d. Based on the graph, this is a negative relationship.
a, b, and c is wrong but d is correct
Apologies for the incorrect response. Let's reevaluate the graph:
Graph: (0,5), (3,3), (6,1)
a. To find the y-intercept, we need to determine the value of y when x is equal to 0. From the given points, we can see that the y-coordinate is 5 when x is 0.
b. To find the slope, we can use the formula: slope = (change in y) / (change in x). From the points (0,5) to (3,3), the change in y is 3 - 5 = -2, and the change in x is 3 - 0 = 3. Thus, the slope is -2/3.
c. The equation of the line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. By substituting the values we found, the equation is y = (-2/3)x + 5.
d. Based on the slope (-2/3), we can determine that this is a negative relationship.
is a 0,5 or 5,0?
Apologies for the confusion. The point notation indicates the coordinates as (x,y). Therefore, in this case, the point (0,5) means that the y-coordinate is 5 when x is equal to 0. Therefore, the correct answer to part a is:
a. The y-intercept is 5.
a. The y-intercept is the value of y when x = 0. In this case, the point with x = 0 is (0,5). Therefore, the y-intercept is 5.
b. The slope of a line can be calculated by finding the change in y divided by the change in x between any two points on the line. Taking the points (0,5) and (6,1), we get:
slope = (change in y) / (change in x) = (1 - 5) / (6 - 0) = -4 / 6 = -2/3
Therefore, the slope of the line is -2/3.
c. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Substituting the values we found, the equation of the line is:
y = (-2/3)x + 5.
d. This is a linear relationship.
To find the answers to these questions, we need to understand the information provided by the graph.
a. The y-intercept is the point where the line crosses the y-axis. In this case, the y-intercept is the point (0, 5) because the value of x is 0 and the corresponding y-value is 5.
b. The slope is a measure of how steep the line is, and it is found by dividing the change in y-values by the change in x-values between any two points on the line. In this case, we can choose any two points on the line. Let's use the points (0, 5) and (3, 3) to calculate the slope. The formula for slope is:
slope = (y2 - y1) / (x2 - x1)
slope = (3 - 5) / (3 - 0)
slope = -2 / 3
So, the slope of the line is -2/3.
c. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. We already have the values for m (-2/3) and b (5). Plugging these values into the equation, we get:
y = (-2/3)x + 5
So, the equation of the line in slope-intercept form is y = (-2/3)x + 5.
d. Based on the given information, we can say that this is a linear relationship. A linear relationship represents a straight line on a graph, and the equation of the line can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation y = (-2/3)x + 5 fits this form, confirming that it is a linear relationship.