the graph of a function is a straight lie with a slope of 2 and a y-intercept of 7. what si the equation of the function? write the answer in y=mx+b form
11 answers
y = 2x + 7
the equation of a function is y=-7x-12 if this function were graphed what would the slope be?
The slope of the function y = -7x - 12 is -7.
write the equation of a linear function that models the relationship shown int he table. Enter the answer in y=mx+b form
TABLE:
(x:11,20)
(y:58,103)
TABLE:
(x:11,20)
(y:58,103)
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
m = (103 - 58) / (20 - 11)
m = 45 / 9
m = 5
Next, we use the slope and one of the points to find the y-intercept. Let's use the point (11, 58):
y = mx + b
58 = 5(11) + b
58 = 55 + b
b = 3
Therefore, the equation of the linear function is:
y = 5x + 3
m = (y2 - y1) / (x2 - x1)
m = (103 - 58) / (20 - 11)
m = 45 / 9
m = 5
Next, we use the slope and one of the points to find the y-intercept. Let's use the point (11, 58):
y = mx + b
58 = 5(11) + b
58 = 55 + b
b = 3
Therefore, the equation of the linear function is:
y = 5x + 3
write the equation of the linear function shown on the graph enre the answer in y=mx+b form
(2,4) (-3,-1)
(2,4) (-3,-1)
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
m = (-1 - 4) / (-3 - 2)
m = -5 / -5
m = 1
Next, we use the slope and one of the points to find the y-intercept. Let's use the point (2, 4):
y = mx + b
4 = 1(2) + b
4 = 2 + b
b = 2
Therefore, the equation of the linear function is:
y = x + 2
m = (y2 - y1) / (x2 - x1)
m = (-1 - 4) / (-3 - 2)
m = -5 / -5
m = 1
Next, we use the slope and one of the points to find the y-intercept. Let's use the point (2, 4):
y = mx + b
4 = 1(2) + b
4 = 2 + b
b = 2
Therefore, the equation of the linear function is:
y = x + 2
yesterday Lump Space Princess worked for 6 hours and earned 120$ LSP worked 8 hours and earned 156$ write the equation of the linear function that models the relationship between the number of hours LSP works and the amount of money she earns.enter the answer in y=mx+b form
To determine the linear function that models the relationship between the number of hours LSP works and the amount of money she earns, we first need to calculate the slope:
Slope (m) = (Change in y) / (Change in x) = (156 - 120) / (8 - 6) = 36 / 2 = 18
Now, we can use the point-slope form of a linear equation to determine the equation in the form y = mx + b. Let's use the point (6, 120) as one point on the line:
y - 120 = 18(x - 6)
y - 120 = 18x - 108
y = 18x + 12
Therefore, the equation of the linear function that models the relationship between the number of hours LSP works and the amount of money she earns is:
y = 18x + 12
Slope (m) = (Change in y) / (Change in x) = (156 - 120) / (8 - 6) = 36 / 2 = 18
Now, we can use the point-slope form of a linear equation to determine the equation in the form y = mx + b. Let's use the point (6, 120) as one point on the line:
y - 120 = 18(x - 6)
y - 120 = 18x - 108
y = 18x + 12
Therefore, the equation of the linear function that models the relationship between the number of hours LSP works and the amount of money she earns is:
y = 18x + 12
interpret the equation y=-4x+10 what type of function does the equation define? describe its graph.
The equation y = -4x + 10 represents a linear function, specifically a linear equation in slope-intercept form. In this equation:
- The coefficient of x (-4) represents the slope of the line.
- The constant term (10) represents the y-intercept, the point where the line crosses the y-axis when x=0.
The graph of a linear function of this form is a straight line with a slope of -4, indicating that for every increase of 1 in x, y decreases by 4 units. The y-intercept is at y=10, meaning that the line crosses the y-axis at the point (0,10).
The line will slant downwards from the left to the right due to the negative slope, with points on the line following a pattern where as x increases, y decreases at a rate of 4 units per 1-unit increase in x.
- The coefficient of x (-4) represents the slope of the line.
- The constant term (10) represents the y-intercept, the point where the line crosses the y-axis when x=0.
The graph of a linear function of this form is a straight line with a slope of -4, indicating that for every increase of 1 in x, y decreases by 4 units. The y-intercept is at y=10, meaning that the line crosses the y-axis at the point (0,10).
The line will slant downwards from the left to the right due to the negative slope, with points on the line following a pattern where as x increases, y decreases at a rate of 4 units per 1-unit increase in x.
1 answer