Answer:
B, C, E, F
Skills needed: Linear Equations
Step-by-step explanation:
Select the four points that appear on the line with the given slope and y-intercept. Slope= 2/3 y-intercept= -7 ———— options = A(2,3) B (9,-1) C(0,-7) D(1,7) E(3,-5) F(6,-3)
1) First, let's create an equation with the information given. I prefer slope-intercept form for this, but other forms (such as point-slope) work as well.
---> Slope intercept form is: [tex]y=mx+b[/tex]
[tex]y = yvalues[/tex]
[tex]m=slope[/tex]
[tex]x=xvalues[/tex]
[tex]b=yintercept[/tex]
We can plug in point values for y and x (and substitute in actual values for b and m) to check if the point is on the line.
2) Let's make the equation:
[tex]y = \frac{2}{3}x-7[/tex], as slope is [tex]\frac{2}{3}[/tex] and y-intercept is -7
Now we can plug in coordinate points and check if they work.
3) Plugging in points
Point A has an x-value of 2, y-value of 3
---> [tex]3=\frac{2}{3}*2-7 \\ 3=\frac{4}{3}-7 \\ 3\neq -5\frac{2}{3}[/tex]
A is not on the line (since both sides are not equal)
Point B has an x-value of 9, y-value of -1
---> [tex]-1=\frac{2}{3}*9-7 \\ -1=6-7 \\ -1=-1[/tex]
B is a point on the line (since both sides are equal)
*IMPORTANT*
C is a point on the line since it is the y-intercept (the y-intercept is when the x-value is 0). (0, -7) is the y-intercept, since the problem states the y-intercept is -7.
Point D has an x-value of 1, y-value of 7
---> [tex]7=\frac{2}{3}*1-7 \\ 7=\frac{2}{3}-7 \\ 7 \neq -6\frac{1}{3}[/tex]
D is not on the line (since both sides are not equal)
NOW
Using process of elimination, we know that E and F are on the line. This is because A and D are not on the line, and we need to select 4 points. We have B and C, and need two more. E and F are the only ones left, so they must be on the line (you can double-check if needed)
Therefore:
Answer is: B, C, E, F
