Graph points:
(0, 5)
(3, 3)
(0, 1)
(4 points)
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 ___ relationship.
y = - 2/3 * x + 5
non proportional
(0, 0)
y = 2/3 * x + 5
y = 5x - 2
y = - 32x + 5
m(0, 5)
m(- 5, 0)
# y = 5x + 2/3
#7
- 2/3
- 5/3
proportional
#0
a. The y-intercept is 5.
b. The slope is -2/3.
c. The equation of the line in slope-intercept form is y = -2/3 * x + 5.
d. This is a non-proportional relationship.
a. To find the y-intercept, we look at the point where the line intersects the y-axis. In this case, the y-intercept is the y-coordinate of the point (0, 5). Therefore, the y-intercept is 5.
b. To find the slope, we use the formula: slope = (change in y) / (change in x). We can use any two of the given points to calculate the slope. Let's use the points (0, 5) and (3, 3):
slope = (3 - 5) / (3 - 0) = -2 / 3
Therefore, the slope 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. Using the values we found in parts a and b, we have:
y = -2/3 * x + 5
So, the equation of the line in slope-intercept form is y = -2/3 * x + 5.
d. This is a non-proportional relationship, as the slope is not equal to 0. When the slope is 0, it indicates a proportional relationship. However, in this case, the slope is -2/3, which means the relationship is not proportional.
To graph the given points, plot each point on a coordinate plane using the x and y values. The first point is (0, 5), so locate the point where x = 0 and y = 5. Similarly, plot the other points (3, 3) and (0, 1) on the graph.
a. To find the y-intercept, identify the point where the line intersects the y-axis. In this case, it can be seen that the line intersects the y-axis at y = 5.
b. To find the slope, select any two points on the line and use the following formula: slope = (change in y)/(change in x). You can choose the points (0, 5) and (3, 3). So the slope is (-2)/(3) or -2/3.
c. To write the equation of the line in slope-intercept form (y = mx + b), use the known y-intercept (b = 5) and slope (m = -2/3). The equation is y = -2/3x + 5.
d. Based on the given equation y = -2/3x + 5, this relationship is non-proportional, as the x and y values do not have a constant ratio or proportionality.