Write the equation of a line in slope intercept form that is parallel to the line y= 1/3x+ 5 and passes through (-9, 5). Do not use any spaces. Slope should be a reduced improper fraction.
slope is 1/3
use the point given in y=1/3 x +b to solve for b.
Now you have the equation
Equations of a straight line :
y = m x + b
Where :
m = slope
b = the y intercept ( where the line crosses the y axis )
Parallel lines have the same slope.
In this case m = 1 / 3
y = ( 1 / 3 ) x + b
x = - 9
y = 5
5 = ( 1 / 3 ) ( - 9 ) + b
5 = - 3 + b Add 3 to both sides
5 + 3 = - 3 + b + 3
8 = b
b = 8
y = m x + b
y = ( 1 / 3 ) x + 8
To find the equation of a line that is parallel to the line y = 1/3x + 5, we need to use the same slope.
The slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the original line has a slope of 1/3, we can use this slope to write the equation of the parallel line.
Using the point-slope form of a line, which is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line, we can substitute the values of the given point (-9, 5) and the slope (1/3) to find the equation.
Using the point-slope form:
y - 5 = 1/3(x - (-9))
y - 5 = 1/3(x + 9)
y - 5 = 1/3x + 3
y = 1/3x + 3 + 5
y = 1/3x + 8
Therefore, the equation of the line that is parallel to y = 1/3x + 5 and passes through (-9, 5) is y = 1/3x + 8.
To find the equation of a line parallel to y = (1/3)x + 5, we need to use the fact that parallel lines have the same slope.
The given line has a slope of 1/3. So, the line we want to find must also have a slope of 1/3.
The slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept.
We have the slope, m = 1/3, and we also know that the line passes through the point (-9, 5).
To find the y-intercept, we can substitute the coordinates of the given point into the equation and solve for b.
5 = (1/3)(-9) + b
First, multiply 1/3 by -9:
5 = -3 + b
Next, isolate b by adding 3 to both sides of the equation:
8 = b
Now we have the slope, m = 1/3, and the y-intercept, b = 8. We can substitute these values into the slope-intercept form equation to get the final equation of the line:
y = (1/3)x + 8