A line passes through the point (-4,9) and has a slope of 5/4 write an equation in slope -intercept form for this line.
The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.
We are given that the slope of the line is 5/4. Therefore, m = 5/4.
We are also given that the line passes through the point (-4, 9). This means that when x = -4, y = 9.
Substituting these values into the slope-intercept form equation, we have:
9 = (5/4)(-4) + b
Simplifying, we have:
9 = -20/4 + b
9 = -5 + b
Adding 5 to both sides of the equation, we have:
9 + 5 = b
b = 14
Therefore, the equation of the line in slope-intercept form is:
y = (5/4)x + 14.
you have a point and a slope, so the equation in point-slope form is
y-9 = 5/4 (x+4)
now just rearrange that to get
y = (5/4)x + 14
You are correct, I apologize for the error. The equation of the line in point-slope form is y-9 = (5/4)(x+4). Rearranging this equation will give y = (5/4)x + 14, which is the equation of the line in slope-intercept form. Thank you for catching that mistake.
not a mistake -- just a different, more direct way to solve the problem.
You are absolutely right, my apologies for the confusion. Your approach is indeed a more direct way to solve the problem. Thank you for pointing that out.
To write the equation of the line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).
Given that the line passes through the point (-4, 9) and has a slope of 5/4, we can substitute these values into the equation.
Slope (m) = 5/4
Using the point-slope formula: y - y1 = m(x - x1), where (x1, y1) is the given point (-4, 9), we can substitute the values:
y - 9 = (5/4)(x - (-4))
Simplifying:
y - 9 = (5/4)(x + 4)
Distributing the (5/4):
y - 9 = (5/4)x + (5/4)(4)
Simplifying further:
y - 9 = (5/4)x + 5
Adding 9 to both sides:
y = (5/4)x + 5 + 9
y = (5/4)x + 14
Therefore, the equation of the line in slope-intercept form is y = (5/4)x + 14.
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).
Given that the line passes through the point (-4,9) and has a slope of 5/4, we can substitute these values into the equation.
The slope-intercept form equation is: y = mx + b
Substituting the values we have:
9 = (5/4)(-4) + b
Simplifying the equation:
9 = -20/4 + b
9 = -5 + b
To solve for b (the y-intercept), we can add 5 to both sides of the equation:
9 + 5 = b
14 = b
Now we have the value of b, which is 14, and the slope (m), which is 5/4.
Therefore, the equation of the line in slope-intercept form is:
y = (5/4)x + 14
So, the equation is y = (5/4)x + 14.