Linear function k has a zero of −3 and a y-intercept of 4 .
Which graph best represents k ?
7 answers
The graph would be a straight line passing through the point (0,4) and intersecting the x-axis at the point (-3,0). The correct graph would be a line slanting upwards to the right and passing through these two points.
The graph of a linear function, f , is shown.
What is the zero of f ?
4
2
-3
-2
What is the zero of f ?
4
2
-3
-2
The zero of a function is the x-value at which the function intersects the x-axis. Looking at the graph, we see that the function intersects the x-axis at 2. Therefore, the correct answer is:
2
2
The graph of linear function g passes through the points (−7,−4) and (7,6) as shown.
What are the slope and y-intercept of the graph g ? Theslopeis 57andthey-interceptis−1
Theslopeis 57andthey-interceptis1 Theslopeis 75andthey-interceptis−1 Theslopeis 75andthey-interceptis1
What are the slope and y-intercept of the graph g ? Theslopeis 57andthey-interceptis−1
Theslopeis 57andthey-interceptis1 Theslopeis 75andthey-interceptis−1 Theslopeis 75andthey-interceptis1
To find the slope and y-intercept of the linear function g, we first need to calculate the slope using the formula:
slope = (change in y) / (change in x)
Given two points (-7, -4) and (7, 6), the change in y is 6 - (-4) = 10 and the change in x is 7 - (-7) = 14. Therefore, the slope is:
slope = 10 / 14 = 5/7
So, the slope of the graph g is 5/7. Now, we can use the point-slope form of a linear equation to find the y-intercept. Using the point (-7, -4) and the calculated slope, we get:
y - y1 = m(x - x1)
y - (-4) = (5/7)(x - (-7))
y + 4 = (5/7)(x + 7)
y + 4 = (5/7)x + 35/7
y = (5/7)x + 35/7 - 4
y = (5/7)x + 35/7 - 28/7
y = (5/7)x + 7/7
y = (5/7)x + 1
Therefore, the slope of g is 5/7 and the y-intercept is 1. The correct answer is:
The slope is 5/7 and the y-intercept is 1.
slope = (change in y) / (change in x)
Given two points (-7, -4) and (7, 6), the change in y is 6 - (-4) = 10 and the change in x is 7 - (-7) = 14. Therefore, the slope is:
slope = 10 / 14 = 5/7
So, the slope of the graph g is 5/7. Now, we can use the point-slope form of a linear equation to find the y-intercept. Using the point (-7, -4) and the calculated slope, we get:
y - y1 = m(x - x1)
y - (-4) = (5/7)(x - (-7))
y + 4 = (5/7)(x + 7)
y + 4 = (5/7)x + 35/7
y = (5/7)x + 35/7 - 4
y = (5/7)x + 35/7 - 28/7
y = (5/7)x + 7/7
y = (5/7)x + 1
Therefore, the slope of g is 5/7 and the y-intercept is 1. The correct answer is:
The slope is 5/7 and the y-intercept is 1.
Identify the slope and y intercept. Then, graph the linear equation.
y = − 53 x + 6 Beginwith b. b=
Movewith m.m=
y = − 53 x + 6 Beginwith b. b=
Movewith m.m=
In the linear equation in the form y = mx + b, "m" represents the slope of the line, and "b" represents the y-intercept.
Given the equation y = -5/3x + 6, the slope is -5/3 and the y-intercept is 6.
Slope (m) = -5/3
y-intercept (b) = 6
To graph the linear equation, start by plotting the y-intercept at y = 6 on the y-axis. The slope of -5/3 indicates that the line decreases by 5 units in the y-direction for every 3 units it increases in the x-direction.
Therefore:
- Start at the y-intercept (0, 6)
- Move 3 units to the right (since the denominator of the slope is 3)
- Move 5 units down
Repeat this process to plot another point, then draw a line through these two points to represent the graph of the linear equation y = -5/3x + 6.
Given the equation y = -5/3x + 6, the slope is -5/3 and the y-intercept is 6.
Slope (m) = -5/3
y-intercept (b) = 6
To graph the linear equation, start by plotting the y-intercept at y = 6 on the y-axis. The slope of -5/3 indicates that the line decreases by 5 units in the y-direction for every 3 units it increases in the x-direction.
Therefore:
- Start at the y-intercept (0, 6)
- Move 3 units to the right (since the denominator of the slope is 3)
- Move 5 units down
Repeat this process to plot another point, then draw a line through these two points to represent the graph of the linear equation y = -5/3x + 6.
1 answer