I have notes on this from online but they are different from this problem and I don't know how to solve it.
Find the equation of a line with the given information:
slope -5/4 and g(14)=-6
It is asking for,
point slope form,
slope intercept form,
Function form,
if vertical write as, x=#
if horizontal write as, y=#
if g(14) = -6, then that means you have the point (14,-6) on the graph. Using the point-slope form, then, you get
y+6 = -5/4 (x-14)
Now massage that to the slope-intercept form:
y+6 = -5/14 x + 35/2
y = -5/14 x + 23/2
thank you
To find the equation of a line with the given information, we need to use one of the forms of the linear equation: point-slope form, slope-intercept form, or function form.
Let's go step by step to find each form of the equation.
1. Point-Slope Form:
The point-slope form of a linear equation is given by the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope.
Given that the slope (m) is -5/4 and the point (14, -6) lies on the line, we can substitute the values into the point-slope form:
y - (-6) = (-5/4)(x - 14)
y + 6 = (-5/4)(x - 14)
This is the equation of the line in point-slope form.
2. Slope-Intercept Form:
The slope-intercept form of a linear equation is given by the formula: y = mx + b, where m is the slope, and b is the y-intercept.
To convert the equation from the point-slope form to the slope-intercept form, we need to solve for y:
y + 6 = (-5/4)(x - 14)
y = (-5/4)(x - 14) - 6
y = (-5/4)x + (5/2) + 6
y = (-5/4)x + (5/2) + (12/2)
y = (-5/4)x + (17/2)
This is the equation of the line in slope-intercept form.
3. Function Form:
The function form of a linear equation is given by the formula: f(x) = mx + b.
Using the equation in slope-intercept form, we can write the function form as:
f(x) = (-5/4)x + (17/2)
This is the equation of the line in function form.
Lastly, we need to determine if the line is vertical or horizontal.
Since none of the forms of the equation have an expression for x or y set to a constant, we can conclude that the line is neither vertical nor horizontal.
I hope this explanation helps you understand how to find the equation of a line given the slope and a point. If you have any further questions, feel free to ask.