Using the graph, derive the equation of the line in slope-intercept form, (0, -4),(1, -1)
The correct answer for math grade 8 unit 4 lesson 8 is
1) y = 3x - 4
2) y = -5x + 1
3) graph (0,2) (1, -1)
4) No, it is not the correct graph because this graph used (0,3) as the y-intercept.
5) graph (3, 1) (0, -1)
Thank you for providing the correct answer key for the math problem. Here is a summary based on the correct answers you provided:
1) The equation of the line in slope-intercept form is y = 3x - 4.
2) The equation of the line in slope-intercept form is y = -5x + 1.
3) The correct graph for the points (0,2) and (1,-1) should match the line y = 3x - 4.
4) The graph using the points (0,3) and (3,2) does not match the line y = -⅓x + 4 because 0,3 is not on the line.
5) The correct graph for the points (3,1) and (0,-1) should match the line y = -5x + 1.
Thank you for the clarification, and let me know if you need any further assistance!
To find the equation of the line in slope-intercept form, we first need to find the slope of the line using the two points given.
Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (-1 -(-4)) / (1 - 0)
Slope (m) = 3 / 1
Slope (m) = 3
Now that we have the slope (m = 3), we can use one of the points and the slope to find the y-intercept (b).
Using the point (1, -1):
-1 = 3(1) + b
b = -4
Now that we have the slope (m = 3) and the y-intercept (b = -4), we can write the equation of the line in slope-intercept form:
y = mx + b
y = 3x - 4
Therefore, the equation of the line in slope-intercept form is y = 3x - 4.
Write the equation of the line in slope-intercept form. (1, -4) (0, 1)
To find the equation of the line in slope-intercept form, we first need to find the slope of the line using the two points provided.
Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (1 - (-4)) / (0 - 1)
Slope (m) = 5 / (-1)
Slope (m) = -5
Now that we have the slope (m = -5), we can use one of the points and the slope to find the y-intercept (b).
Using the point (1, -4):
-4 = -5(1) + b
-4 = -5 + b
b = 1
Now that we have the slope (m = -5) and the y-intercept (b = 1), we can write the equation of the line in slope-intercept form:
y = mx + b
y = -5x + 1
Therefore, the equation of the line in slope-intercept form is y = -5x + 1.
(0,3) (3, 2) Is this the correct graph of y = -⅓x + 4
To determine if the given points (0,3) and (3,2) lie on the graph of y = -⅓x + 4, we can substitute the x and y values of each point into the equation to see if they satisfy it.
For the point (0,3):
y = -⅓(0) + 4
y = 4
The y-value of the equation is 4, while the y-value of the point is 3. Therefore, the point (0,3) does not lie on the graph.
For the point (3,2):
y = -⅓(3) + 4
y = 4 - 1
y = 3
The y-value of the equation at x = 3 is 3, which matches the y-value of the point (3,2). Hence, the point (3,2) lies on the graph of y = -⅓x + 4.
Therefore, the graph of y = -⅓x + 4, the given points (0,3) and (3,2) lie exactly on the line for y = -⅓x + 4.