Slope From A Table, Graph & Equation

The bigger the number the steeper the line.

The linear parent function is y = x because it represents a straight line with a slope of 1 and passes through the origin (0,0). In this function, the value of y is always equal to the value of x, which makes it a simple and basic representation of a linear relationship. Therefore, the given statement is true.

Slope is the m in the equation mx + b..... so 9 is the slope.

The y-intercept of a line is the point where the line intersects the y-axis. In the equation y = 2x + 4, the constant term 4 represents the y-coordinate of the y-intercept. Therefore, the y-intercept is at the point (0,4).

The correct function for the given description is y=1/4x + 2. This function represents a linear relationship with a slope of 1/4, meaning that for every increase of 1 in the x-coordinate, the y-coordinate increases by 1/4. The y-intercept is (0,2), which means that the line crosses the y-axis at y=2. Therefore, the equation y=1/4x + 2 satisfies both the slope and y-intercept conditions.

The correct answer is that the linear function has a slope of 3 and a y-intercept of (0, -5). This means that for every increase of 1 in the x-coordinate, the y-coordinate will increase by 3. The y-intercept is the point where the line crosses the y-axis, which in this case is at (0, -5).

The correct answer is that the second function shifted 10 units down. This can be determined by comparing the two functions. In the first function, y = 2x + 5, the constant term is +5, indicating that the graph of the function intersects the y-axis at the point (0, 5). In the second function, y = 2x - 5, the constant term is -5, indicating that the graph of the function intersects the y-axis at the point (0, -5). Since the constant term changed from +5 to -5, the function shifted 10 units down.

The slope of a line is determined by the change in the y-coordinates divided by the change in the x-coordinates between two points on the line. In this case, the change in y is -2 (2 - 0) and the change in x is -1 (1 - 2). Therefore, the slope is -2/-1, which simplifies to 2.