Answer:
To find the slope, we can use the fact that the line passes through (5, 8) and has an x-intercept of 6. This means that the line also passes through (6, 0). The slope formula is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. Using the given points, we get m = (0 - 8) / (6 - 5) = -8.
To write the equation in point-slope form, we can use the formula y - y1 = m (x - x1), where m is the slope and (x1, y1) is any point on the line. We can use either of the given points, but let’s use (5, 8) for simplicity. Plugging in the values, we get y - 8 = -8 (x - 5).
To write the equation in slope-intercept form, we need to find the y-intercept, which is the value of y when x is zero. We can do this by plugging in x = 0 into either of the equations we have so far. For example, using the point-slope form, we get y - 8 = -8 (0 - 5), which simplifies to y = 32. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Substituting the values we found, we get y = -8x + 32.
Therefore, the equation of the line in point-slope form is y - 8 = -8 (x - 5) and in slope-intercept form is y = -8x + 32. You can check your answers by graphing the line using an online tool such as this one. You should see that the line passes through (5, 8) and (6, 0) as expected
Explanation: