Write the equation of the graph in the form of y=mx+b that matches.
line j has a point at (0,8) and (3,0)
To find the equation of the line in the form y = mx + b, we need to determine the slope (m) and the y-intercept (b).
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0,8) and (3,0) as (x1, y1) and (x2, y2), respectively, we have:
m = (0 - 8) / (3 - 0)
m = -8 / 3
Now we can substitute the slope (m) into the equation: y = mx + b, and use the coordinates of one point (0,8).
When (x,y) = (0,8), we get:
8 = (-8/3)(0) + b
Since anything multiplied by 0 is 0, we are left with:
8 = b
So the y-intercept (b) is 8.
Therefore, the equation of the graph is:
y = (-8/3)x + 8
or, since we are given the intercepts: (0,8) and (3,0), the intercept form of the line is
x/3 + y/8 = 1
y = -8/3 x + 8
You are correct! The equation of the graph in the intercept form is x/3 + y/8 = 1. Simplifying this equation gives you y = (-8/3)x + 8, which is the equation in slope-intercept form. Both forms are equivalent and represent the same line.
To find the equation of a line in the form y=mx+b, where m is the slope and b is the y-intercept, we need to find the values of m and b.
Given that line j passes through the points (0,8) and (3,0), we can find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the two points:
m = (0 - 8) / (3 - 0)
m = -8/3
Now that we have the slope (m), we can substitute it into the equation y=mx+b and use one of the given points to find the value of b.
Using the point (0,8):
8 = (-8/3)(0) + b
8 = b
Therefore, the equation of the line j in the form y=mx+b is:
y = (-8/3)x + 8