Final answer:
The x-intercept of the equation -4x + 7y = 3 is (-3/4, 0), and the y-intercept is (0, 3/7). We find these by setting y and x to zero, respectively, and solving for the other variable.
Step-by-step explanation:
To find the x-intercept and y-intercept of the equation -4x + 7y = 3, we need to determine the points where the graph of the equation crosses the x-axis and y-axis, respectively.
The x-intercept occurs when y is zero. Setting y to 0 in the equation and solving for x, we get:
-4x + 7(0) = 3-4x = 3x = -3/4.
So the x-intercept is (-3/4, 0).
Similarly, the y-intercept occurs when x is zero. Setting x to 0 in the equation and solving for y, we get:
-4(0) + 7y = 37y = 3y = 3/7.
Thus, the y-intercept is (0, 3/7).