Question

A system of linear equations is represented by line j and line k.

3. A table representing some points on line j and the graph of line k are shown.
X
y
-8
15
Line /
-3
10
1
10
6
3
4
10
-6
Line k
AY
2
4
x
Which system of equations is best represented by lines j and k?

Answer 1

The system of equations that is best represented by lines j and k is: y = -x + 7 and y = 2/3x - 1.

What is the system of equations?

To get the system of equations for both lines, express their equations in slope-intercept form (y = mx + b) by finding the slope (m) and y-intercept (b) for each of the lines.

Equation for line j:

Slope (m) = change in y / change in x = 6 - 4 / 1 - 3

m = -1

To find the y-intercept, substitute a point (1, 6) = (x, y) and the slope (m = -1) into y = mx + b:

6 = -1(1) + b

6 = -1 + b

6 + 1 = b

b = 7

Substitute m = -1 and b = 7 into y = mx + b to get the equation for line j:

y = -x + 7

Equation for line k:

Slope (m) = 8/12

m = 2/3

y-intercept (b) = -1.

The equation for line k is: y = 2/3x - 1

The system is: y = -x + 7 and y = 2/3x - 1