Final answer:
The slope and intercepts of the equation 7x+14y-2=0 are -1/2 and 1/7, respectively. To sketch the line, plot the y-intercept and use the slope to find one or more additional points. Then, connect the points with a straight line.
Step-by-step explanation:
To find the slope and intercepts of the equation 7x+14y-2=0, we can rearrange it to the slope-intercept form y=mx+b, where m is the slope and b is the y-intercept. So, let's rearrange the equation: 14y=-7x+2. Dividing by 14, we get y=(-7/14)x+2/14. Simplifying further, y=(-1/2)x+1/7. Therefore, the slope of the line is -1/2 and the y-intercept is 1/7.
To sketch the line, we can use the slope-intercept form. Start by plotting the y-intercept at (0, 1/7). Then, use the slope, which is -1/2, to find another point on the line. The slope tells us that for every increase of 1 on the horizontal axis, the line decreases by 1/2 on the vertical axis. So, from the y-intercept, move 1 unit to the right and 1/2 unit down. Plot this point, and repeat the process to find more points if desired. Finally, connect the points with a straight line to complete the sketch.