Question

A.3(f) The line graphed on the grid represents the first of two equations in a system of linear equations.

20
-16
12
-8
-20 -16 -12
-
-4
48
12
16 2024
-8
-12
16
If the graph of the second equation in the system passes through (-12, 20) and (4,12), which statement is true?

Answer 1

I don’t any idea for this

Answer 2

If the graph of the second equation in the system passes through the points (-12, 20) and (4, 12), a statement that is true is: C. The system has no solution.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

`Slope(m)=(y_2-y_1)/(x_2-x_1)`

By substituting the given data points (-12, 20) and (4, 12) into the formula for the slope of a line, the slope of the second equation is given by;

Slope (m) = (12 - 20)/(4 + 12)

Slope (m) = -8/16

Slope (m) = -1/2

For the slope of the first line, we have:

Slope (m) = rise/run

Slope (m) = -10/20

Slope (m) = -1/2

Since the slope of the two lines are the same, it means they are parallel lines and would have no solution because they can never intersect.

Complete Question:

The line graphed on the grid represents the first of two equations in a system of linear equations.

If the graph of the second equation in the system passes through the points (-12, 20) and (4, 12), which statement is true?

The only solution to the system is (10,5).

The only solution to the system is (0,14).

The system has no solution.

The system has an infinite number of solutions.