Answer:
AB: y=2x+2
CB: y=-2x+6
CD: y=1/2x-1.5
DA: y=-3x+2
Step-by-step explanation:
Answer:
AB: [tex]y=2x+2[/tex]
CB: [tex]y=-2x+6[/tex]
CD: [tex]y=\frac{1}{2}x -1.5[/tex]
DA: [tex]y=-3x+2[/tex]
Step-by-step explanation:
So when it's saying y = __ x + __ it's asking for the slope-intercept form. This is given as y=mx+b where m is the slope and b is the y-intercept. m is the slope because as x increases by 1, the y-value will increase by m, which is by definition what the slope is [tex]\frac{rise}{run}[/tex] how much the function "rises" as x "runs".
AB: See how it "rises" by 2 and only "runs by 1", thus the slope is 2/1 or 2. the last part is the y-intercept, which is the value of y when the line crosses the y-axis. If you look at the graph when it "crosses" the y-axis it's y-value is 2. So you have the equation: [tex]y=2x+2[/tex]
CB: See how it "goes down" by 4 and "runs" by 2, thus the slope is -4/2 or -2. The y-intercept isn't shown on the graph but you can calculate that by substituting known values into the slope-intercept form. So we know so far y=-2x+b since the slope was calculated, and we can take any point on the line to calculate b, for this example I'll take the point C which is (3, 0) which is (x, y) and I'll plug that in
Plug values in:
0 = -2(3) + b
0 = -6 + b
6 = b
This gives you the complete equation: [tex]y=-2x+6[/tex]
CD: see how it only "rises" by 1 but "runs" by 2, thus the slope is 1/2. The y-intercept isn't shown on the graph but you can calculate it by substituting a point into the equation For this example I'll use point C (3, 0)
0 = 3(1/2) + b
0 = 1.5 + b
-1.5 = b
This gives you the complete equation: [tex]y=\frac{1}{2}x - 1.5[/tex]
DA: see how it "decreases" by 3 but "runs" by 1, thus the slope is -3/1 or -3. The y-intercept is known and is at (0, 2) so now we plug these values in to get the equation: [tex]y=-3x+2[/tex]