Question

graph the function ( h(x) = 2x - 5 ).

Explanation:

Step1: Identify the function type

The function \( h(x) = 2x - 5 \) is a linear function in the form \( y = mx + b \), where \( m = 2 \) (slope) and \( b = -5 \) (y - intercept).

Step2: Find the y - intercept

To find the y - intercept, set \( x = 0 \). Then \( h(0)=2(0)-5=-5 \). So the y - intercept is the point \( (0, - 5) \).

Step3: Find another point using the slope

The slope \( m = 2=\frac{2}{1} \), which means for a run of 1 (increase in x by 1), the rise is 2 (increase in y by 2). Starting from the y - intercept \( (0, - 5) \), if we increase x by 1 (to \( x = 1 \)) and y by 2 (to \( y=-5 + 2=-3 \)), we get the point \( (1, - 3) \).

Step4: Plot the points and draw the line

Plot the points \( (0, - 5) \) and \( (1, - 3) \) on the coordinate plane. Then draw a straight line passing through these two points. The line should extend in both directions (using the arrow tool if needed) to represent the linear function for all real values of \( x \).

(Note: Since this is a graphing problem, the final answer is the graph of the line passing through \( (0, - 5) \) and \( (1, - 3) \) (and other points determined by the slope) with a slope of 2 and y - intercept at \( (0, - 5) \).)

Answer:

Step1: Identify the function type

The function \( h(x) = 2x - 5 \) is a linear function in the form \( y = mx + b \), where \( m = 2 \) (slope) and \( b = -5 \) (y - intercept).

Step2: Find the y - intercept

To find the y - intercept, set \( x = 0 \). Then \( h(0)=2(0)-5=-5 \). So the y - intercept is the point \( (0, - 5) \).

Step3: Find another point using the slope

The slope \( m = 2=\frac{2}{1} \), which means for a run of 1 (increase in x by 1), the rise is 2 (increase in y by 2). Starting from the y - intercept \( (0, - 5) \), if we increase x by 1 (to \( x = 1 \)) and y by 2 (to \( y=-5 + 2=-3 \)), we get the point \( (1, - 3) \).

Step4: Plot the points and draw the line

Plot the points \( (0, - 5) \) and \( (1, - 3) \) on the coordinate plane. Then draw a straight line passing through these two points. The line should extend in both directions (using the arrow tool if needed) to represent the linear function for all real values of \( x \).

(Note: Since this is a graphing problem, the final answer is the graph of the line passing through \( (0, - 5) \) and \( (1, - 3) \) (and other points determined by the slope) with a slope of 2 and y - intercept at \( (0, - 5) \).)