Which classification describes the system of linear equations?
1 answer:
Answer:
Inconsistent
Step-by-step explanation:
Consistent independent means that there is only one solution; ie one place where the 2 lines intersect.
Inconsistent means that the lines will NEVER cross because they are parallel
Consistent dependent means that the 2 lines, when solved for y, are the exact same line (same slope, same y-intercept)
In our system, one of the equations is already solved for y, so let's solve the other one for y:
so
and
The slopes of the 2 lines are the same; therefore, they are parallel and will never intersect. Inconsistent system.
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Hi! I'm happy to help!
Point slope form states that y-=m(x-
). m represents your slope (rise/run) and
and
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.
<u>You should pick option 3.</u>
<u>(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.)</u>
I hope this was helpful, keep learning! :D