Question

17. what is the equation of the line with…

Answer 1

`y=\displaystyle (1)/(2)x+1`

Explanation:

Linear equations are typically organized in slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept.

We're given the x-intercept, -2, and the y-intercept, 1. We can directly plug the y-intercept into the equation
`y=mx+b` :

`y=mx+1`

Now, we must solve for the slope. The x-intercept -2 gives us the point (-2,0), since the x-intercept occurs when y=0. Plug this point into the equation and solve for m:

`0=m(-2)+1\\0=-2m+1\\-1=-2m\\\\\displaystyle m=(-1)/(-2) \\\\\displaystyle m=(1)/(2)`

Therefore, the slope of the line is
`\displaystyle (1)/(2)`. Plug this back into
`y=mx+1`:

`y=\displaystyle (1)/(2)x+1`

I hope this helps!