A line has slope 16/5 and passes through the point (-2,-5)

Question

1. By substituting into the equation y=mx+b, find the value of b for this line.
2. Write the equation of the line in standard form.

Answer 1

Hello Luna!

Good old linear equations! This can be very challenging but let's see if I can help you through this.

Step 1:

We are given two important pieces of information: the slope (m) and a point (x, y). Slope-intercept form of an equation is y = mx + b. We are given the values of 3 of the 4 letters! LET'S PLUG 'EM IN!

y = mx + b ---> -5 = 16/5*-2 + b [I'll record a video version as typing fractions is ugly]

Step 2:

Now that we have an equation with just one variable (b AKA the y-intercept), we can solve it!

-5 = 16/5 * -2 + b

-5 = -32/5 + b [16/5 * -2 = -32/5]

7/5 = b THIS IS THE ANSWER FOR #1!

Step 3:

Now that we know b, we can rewrite the equation from slope-intercept to standard form

y = 16/5 * x + 7/5

Standard form is Ax + By = C [in other words, the x and y terms are on the left side]

To make this into standard form, we need to, we need to move the 16/5*x over by doing the opposite to both sides [which is -16/5 x + 7/5]

Once we do that, we have the answer!

-16/5*x + y = 7/5

*Some math people believe that the front number can't be negative so you could multiply everything by a negative 1 to make it 16/5*x - y = -7/5.

Answer 2

1) The slope is 16/5 so substitute that in for m

y = 16/5*x + b

Next, we're also given a point (-2, -5). This means that when x = -2, y = -5. Thus, we can plug these in for x and y.

(-5) = 16/5*(-2) + b.

Solve for b:

-5 = -32/5 + b

32/5 - 5 = b

7/5 = b

2) Rewrite y = mx + b with the slope and the y-intercept that we just found

Answer 3

1-)

m=16/5

For x we can use -2

For y we can use -5

-5=16/5(-2)+b

-5=-32/5+b add 32/5 to the both side

-5+32/5= -32/5+32/5+b

-5+32/5= b find the same denominator

-25/5+32/5=b

b= 7/5

2) y= 16/5 x + 7/5