Question

The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y - 4 = 1/4(x- 8). What

Answer 1

Hi! I'm happy to help!

Point slope form states that y-$y_{1}$=m(x-$x_{1}$). m represents your slope (rise/run) and $y_{1}$ and $x_{1}$ represent your first y and x points, and y and x represent your second y and x points. We already have our equation here:

y - 4 = 1/4(x- 8)

Now, let's dive into what slope-intercept form is. Slope intercept form states that y=mx+b. m represents our slope, b represents our y intercept, y represents a y point, and x represents the corresponding x point.

Since we know our m, we can solve for b, by using our other numbers. Let's use our first set of coordinates.

4=1/4(8)+b

4=2+b

2=b

Now our second set to double check:

2=1/4(0)+b

2=0+b

2=b

We know that b must equal 2, so our equation must be y=1/4x+2, which is  option 3.

You should pick option 3.

(y-intercept is where the line hits the y-axis(when x=0). We could've used our second coordinates (0,2), where x equals 0 to know that 2 is the y-intercept (b). This shortcut only works on specific problems though.)

I hope this was helpful, keep learning! :D