Question

What is the equation of the line that passes through the point (-7, -7) and
has a slope of 1?

Answer 1

`y=x`

Explanation:

Hi there!

What we need to know:

• Linear equations are typically organized in slope-intercept form:
  `y=mx+b` where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis
• y and x stay as they are while m and b are replaced with numerical values

1) Determine the slope (m)

`y=mx+b`

We're given that the slope of the line is 1. Plug this into the above equation

`y=1x+b\\y=x+b`

2) Determine the y-intercept (b)

`y=x+b`

Plug in the given point (-7,-7)

`-7=-7+b`

Add 7 to both sides to isolate b

`-7+7=-7+b+7\\0=b`

Therefore, the y-intercept is 0. Plug this back into
`y=x+b`

`y=x+0\\y=x`

I hope this helps!