Final answer:
The equation y + 5 = x - 3 simplifies to y = x - 8, representing a line with slope 1 and y-intercept -8. To graph an equation like y = 9 + 3x, create a table of values, plot the points, and draw a line through them showing a slope of 3 and y-intercept 9.
Step-by-step explanation:
The student's question involves simplifying an equation. The provided information contains various equations and operations. The correct simplification of the equation y - (-5) = 1(x - 3) is actually y + 5 = x - 3. In this process, the negative sign before the 5 is canceled out by the subtraction, which is equivalent to adding positive 5 to y. Similarly, the 1 multiplying (x - 3) does not change the value and results in simply x - 3. this equation represents a straight line on a graph with a slope (m) of 1 and a y-intercept (b) of -8 (which you get from isolating y to get y = x - 8).
An example for graphing an equation can be derived from the given linear function y = 9 + 3x. To plot this, one would create a table of x and y values, calculate y for each x, and then graph those points on a coordinate plane. The 'b' term here is 9, representing the y-intercept, while the 'm' term is 3, representing the slope of the line. Connecting these points will result in a linear graph.