Final answer:
To find the equation of a line, we need to determine its slope (m) and y-intercept (b). We can use the given points (5, 0) and (4, 3) to find the slope and then substitute the values into the point-slope form of the equation to get the final equation in slope-intercept form: y = -3x + 12.
Step-by-step explanation:
To find the equation of a line, we need to determine its slope (m) and y-intercept (b). We can use the coordinates of the given points (5, 0) and (4, 3) to find the slope. The slope is given by the formula: m = (y2 - y1) / (x2 - x1). Plugging in the values, we get: m = (3 - 0) / (4 - 5) = -3.
Next, we can use the point-slope form of the equation of a line, which is y - y1 = m(x - x1). Choosing one of the given points, let's use (4, 3), we can substitute the values to get: y - 3 = -3(x - 4). Simplifying, we have y - 3 = -3x + 12. Moving the -3x term to the left side, we get y + 3x = 12.
Finally, we can rearrange the equation in slope-intercept form, which is y = mx + b, by subtracting 3x from both sides to get the equation: y = -3x + 12.