Graph the equation 9 − x = 3/2y using slope-intercept form
To graph this equation using the slope-intercept form, we first need to rewrite the equation in the form y = mx + b, where m is the slope and b is the y-intercept.
9 - x = (3/2)y
To isolate y, first we can multiply both sides by 2:
2(9 - x) = 2(3/2)y
18 - 2x = 3y
Now, we can add 2x to both sides:
18 = 3y + 2x
Next, we can divide both sides by 3:
6 = y + (2/3)x
Finally, we have the equation in the slope-intercept form:
y = (2/3)x + 6
Now we can plot the equation. The slope m = 2/3 means that for each unit increase in x, the value of y will increase by 2/3 units. The y-intercept b = 6 means that when x = 0, y = 6.
1. Start at the point (0, 6) on the graph, which represents the y-intercept.
2. From this point, move 1 unit to the right (increase x by 1 unit) and 2/3 units upward (increase y by 2/3 units) to find another point on the line.
3. Repeat this process to plot more points on the line.
Finally, connect the points with a straight line to represent the equation y = (2/3)x + 6.