Final answer:
To graph the equation 3x + 4y = 6, we rewrite it in slope-intercept form y = mx + b and identify the slope and y-intercept. The graph cuts the x-axis at the point (2, 0) and the y-axis at the point (0, 3/2).
Step-by-step explanation:
To graph the linear equation 3x + 4y = 6, we can rewrite it in slope-intercept form y = mx + b where m is the slope and b is the y-intercept. To isolate y, we subtract 3x from both sides and divide by 4, giving us y = -3/4x + 3/2. From this equation, we can see that the slope is -3/4 and the y-intercept is 3/2.
To find the points where the graph cuts the x-axis, we set y = 0 and solve for x. Plugging in y = 0 into the slope-intercept form equation, we get 0 = -3/4x + 3/2. Solving for x, we get x = 2. Therefore, the graph cuts the x-axis at the point (2, 0).
To find the points where the graph cuts the y-axis, we set x = 0 and solve for y. Plugging in x = 0 into the slope-intercept form equation, we get y = 3/2. Therefore, the graph cuts the y-axis at the point (0, 3/2).