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Example of the linear function

Given the function y = -2x + 3, answer the following statements true or false.

Statement 1. The graph of y = -2x + 3 pass through quadrant1, quadrant2, quadrant3.

Statement 2. The graph of y = -2x + 3 pass through the point A (3, -3).

Statement 3. In the graph of y = -2x + 3, the function y increase as x increase.

Statement 4. The coordinate of the intersection point of the graph passing through the x-axis is:

Statement 5. The coordinate of the intersection point of the graph pass through the y-axis is:

Solution:

Solution for statement 1. Draw the graph of y = -2x + 3. Let x = 0, y = 3. Let y = 0, x = 3/2 = 1.5. We get two points (0, 3) and (1.5, 0), draw a line pass through these two points, we get the graph of y = -2x + 3

draw the graph of y = -2x + 3, the function y = -2x + 3 is a linear function.

Look the figure above, the graph of y = -2x + 3 pass the quadrant 1, quadrant 2 and quadrant 4. So, the statement 1 is true.

Solution for statement 2. If point A (3, -3) lies on the graph of y = -2x + 3, then the coordinate of the point A must satisfy the equation y = -2x + 3. Substitute x = 3 and y = -3 to y = -2x + 3 to verify whether the values of x and y satisfy the equation.

when x = 3, y = -2 × 3 + 3 = -6 + 3 = -3, so x = 3, y = -3. The point A lies on the graph of y = -2x + 3. Therefore, the statement 2 is true.

Solution for statement 3. Look the graph of y = -2x + 3, the value of y = -2x + 3 decrease as x increase. Therefore, the statement 3 is false.

Solution for statement 4. When y = 0, the graph pass through the x-axis. Substitute y = 0 into the equation y = -2x + 3. So, 0 = -2x + 3. 2x = 3. x = 3/2 = 1.5. Therefore, the coordinate of the intersection point of the graph passing through the x-axis is 1.5

Solution for statement 5. When x = 0, the graph pass through the y-axis. Substitute x = 0 into the equation y = -2x + 3. If x = 0, y = 3. Therefore, the coordinate of the intersection point of the graph pass through the y-axis is 3.