Answer: y= 8 + (-3/5)x is the equation of the line
Step-by-step explanation:
I would first like to begin solving this problem by identifying the equation for the line which will take the form of:
y = a + bx
where b =slope
a = y-intercept
and x and y represent the x and y coordinates
We are given that the slope is -3/5 so let's plug that into the equation
y = a + (-3/5)x
Now, because we know that (5,5) is indeed a point on the graph, we can also substitute these coordinates into the equation
5 = a + (-3/5)(5)
Now, to fully solve this equation, we need to find the value of a
With some simple algebra, we can isolate the a and find its true value or also known as the y-intercept
(-3/5)(5) = -3
5 = a + (-3)
*Now we will add 3 to both sides
5 + 3 = a + (-3) + 3
5 + 3 = a + 0
8 = a
Hooray! We now have all of our variables so we can now substitute everything into the original equation: y = a + bx
y = 8 + (-3/5)x
Now as a good measure, we can also check that (5,5) is actually a point in the equation by substituting the variables in
5 = 8 + (-3/5)(5)
We know that -3/5 times 5 is -3
5 = 8 + (-3)
5 = 8 -3
5 = 5
This works which means that y= 8 + (-3/5)x is the equation of the line. Hope that helps!
