What is the equation of the line that passes through the point (5,5) and has a slope of -3/5

Answer 1

Hi Gianna,

I hope you are doing well!

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!

Answer 2

-3/5 = slope = (y-5)/(x-5). Difference in y values divided by difference in x values = slope

(-3/5)(x-5) = y-5 is the equation is point slope form

y = (-3/5)x + 3+5 is the linear equation in slope intercept form

y = -3x/5 + 8 is the equation with slope =-3/5 through the point (5,5)

slope is the coefficient of the x term when a linear equation is solved for y

check the answer, plug x=5, y=5 into the equation

5 = -3(5)/5 + 8

5 = -3+8

5+5

or

you could write the equation as

3x +5y = 40 in standard form for a linear equation

or

3x+5y -40 = 0 in general form: ax+by+c = 0 with a=3, b=4, c=-40