Final answer:
The x-coordinate for the x-intercept of the line passing through the points (7,4) and (6,3) is 3.
Step-by-step explanation:
The x-coordinate for the x-intercept of a line can be found by setting the y-coordinate to 0 and solving for x. To find the equation of the line passing through the points (7,4) and (6,3), we can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points, we get m = (3 - 4) / (6 - 7) = -1 / -1 = 1.
Next, we can substitute one of the given points and the slope into the equation y = mx + b and solve for b. Using the point (7,4) and the slope m = 1, we get 4 = 1 * 7 + b. Solving for b, we have b = 4 - 7 = -3.
Now we can write the equation in slope-intercept form: y = 1x - 3. To find the x-coordinate for the x-intercept (where y = 0), we set y = 0 and solve for x. 0 = 1x - 3, so x = 3.