Question

Enter the letters of the points that lie on the line $y = \frac{1}{2} x + 3.$[asy]unitsize(0.4 cm);pair A, B, C, D, E, F, G, H, I, J;int i;A = (3,3);B = (-5,-4);C = (-4,1);D = (6,-1);E = (6,6);F = (-2,-2);G = (-3,5);H = (3,-6);I = (2,4);J = (2,-3);for (i = -8; i <= 8; ++i) {draw((i,-8)--(i,8),gray(0.7));draw((-8,i)--(8,i),gray(0.7));}draw((-8,0)--(8,0),linewidth(1.5*bp),Arrows(6));draw((0,-8)--(0,8),linewidth(1.5*bp),Arrows(6));label("$x$", (8,0), NE);label("$y$", (0,8), NE);dot("$A$", A, SE);dot("$B$", B, S);dot("$C$", C, NW);dot("$D$", D, SE);dot("$E$", E, SE);dot("$F$", F, SE);dot("$G$", G, NW);dot("$H$", H, SE);dot("$I$", I, NW);dot("$J$", J, NE);[/asy]

Answer 1

The points that lie on the line are C(-4, 1), E(-6, 6) and  I(2, 4)

Given the equation of a line expressed as $y=\frac{1}{2}x + 3$

We need to find which of the points from A to J lies on the line.

To do that, we will substitute the x-coordinate point into the equation to see if we are going to get the y-coordinate

For the coordinate C(-4, 1)

when x = -4

y = 1/2(-4) + 3

y = -2 + 3

y = 1

This shows that the point C(-4, 1) is on the line

For the point E(6, 6)

when x = 6

y = 1/2(6) + 3

y = 3 + 3

y = 6

This shows that the point E(-6, 6) is on the line

For the point I (2, 4)

when x = 2

y = 1/2(2) + 3

y = 1 + 3

y = 4

This shows that the point I(2, 4) is on the line

This shows that the points that lie on the line are C(-4, 1), E(-6, 6) and  I(2, 4)

Learn more here: brainly.com/question/16131866