ProblemGraph the function y=−3x+5𝑦=−3𝑥+5. SolutionTo graph the function without making a table, follow these steps:Identify the y𝑦-intercept: b=𝑏= Plot the intercept: (0,(0, ))Identify the slope: m=𝑚= (This is equal to −31−31, so the rise is −3−3 and the run is 11.)Move over 11 unit and down 33 units to find another point on the line: (1,2)(1,2).Draw the line through the points (0,5)(0,5) and (1,2)(1,2).

Sure, here is the step-by-step solution to graph the function y=-3x+5:

1. Identify the y-intercept: The y-intercept is the value of y when x is 0. In this case, the y-intercept (b) is 5. So, we have the point (0,5).

2. Plot the y-intercept: On your graph, plot the point (0,5).

3. Identify the slope: The slope (m) is the coefficient of x, which is -3 in this case. This means for every 1 unit increase in x, y decreases by 3 units (since the slope is negative).

4. Use the slope to find another point: Starting from the y-intercept (0,5), move 1 unit to the right (as the run is 1) and 3 units down (as the rise is -3). This gives us another point on the line, (1,2).

5. Draw the line: Now that we have two points, (0,5) and (1,2), we can draw a line passing through these points. This line represents the function y=-3x+5.