Final answer:
To graph the line from the equation 3x – 4y = 8 using its slope, rewrite the equation in slope-intercept form to find the slope. The slope is 3/4, meaning for every 4 units right, move 3 units up. The correct movement is option B: 4 units up, 3 units to the right.
Step-by-step explanation:
To use the slope of the line to graph the equation 3x – 4y = 8, we first need to find the slope. For the standard form ax + by = c, we can rewrite it in slope-intercept form (y = mx + b) to easily identify the slope (m) and the y-intercept (b). To do this for our equation, we can rearrange it as follows:
4y = 3x - 8
y = (3/4)x - 2
Now, the coefficient of x in the equation, which is (3/4), represents the slope of the line. This means that for every 4 units we move horizontally (to the right, if positive), we move 3 units vertically (up, if the slope is positive). Therefore, the correct movement from one point to another on the line is B. 4 units up, 3 units to the right.