Question

graph the line with the equation $y = 5x - 2$.

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = 5x - 2 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 5 \) (which can be written as \( \frac{5}{1} \)) and \( b=-2 \).

Step2: Plot the y-intercept

The y - intercept \( b=-2 \) means the line crosses the y - axis at the point \( (0,-2) \). Locate the point \( (0, - 2) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m = \frac{5}{1} \) means for every 1 unit we move to the right (increase in \( x \) by 1), we move up 5 units (increase in \( y \) by 5). Starting from \( (0,-2) \), if we move 1 unit to the right (to \( x = 1 \)) and 5 units up, we get to the point \( (1, - 2+5)=(1,3) \). We can also move left 1 unit (decrease \( x \) by 1) and down 5 units (decrease \( y \) by 5) from \( (0,-2) \) to get \( (-1,-2 - 5)=(-1,-7) \).

Step4: Draw the line

Draw a straight line through the points we have plotted (e.g., \( (0,-2) \), \( (1,3) \)) to graph the line \( y = 5x-2 \).

Answer:

The line is graphed by plotting the y - intercept \( (0,-2) \), using the slope \( 5 \) to find another point (e.g., \( (1,3) \)) and then drawing a straight line through these points. The graph should be a straight line with a steep positive slope, crossing the y - axis at \( (0, - 2) \) and passing through points like \( (1,3) \), \( (2,8) \), etc. (or their left - side counterparts like \( (-1,-7) \), \( (-2,-12) \) etc.).