Understand linear equation form: To graph the equation y=−x+19, we need to understand that it is a linear equation in the slope-intercept form y=mx+b, where m is the slope and b is the y-intercept.
Identify slope: The slope m of the line is −1, which means that for every unit increase in x, y decreases by 1 unit. This gives us the direction in which the line moves.
Determine y-intercept: The y-intercept b is 19, which is the point on the y-axis where the line crosses it. This gives us a starting point for drawing the line.
Plot y-intercept: To graph the line, we can start by plotting the y-intercept (0,19) on the graph.
Find another point: Next, we use the slope to find another point. Since the slope is −1, we can go down 1 unit on the y-axis and move 1 unit to the right on the x-axis from the y-intercept. This gives us the point (1,18).
Draw the line: We can now draw a straight line through the points (0,19) and (1,18), extending it in both directions. This line represents the graph of the equation y=−x+19.
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