A linear function has the same y-intercept as x+2y=8 and it’s graph contains the point (9,6) find the y-intercept of the linear function
+37170 arrange in y = mx + b form y = -1/2 x + 4 4 = b = y axis intercept
+23254 Step 1) Find the y-intercept of x + 2y = 8:
Substitute 0 for x in the equation: 0 + 2y = 8 ---> 2y = 8 ---> y = 4
The y-intercept is 4.
Step 2) Find the equation of the new line.
You know that these two points (9, 6) and (0, 4) are on the line.
First, find the slope: m = (y2 - y1) / (x2 - x1) ---> m = (4 - 6) / (0 - 9)
---> m = 2/9
Now, use the point-slope formula: y - y1 = m(x - x1)
---> y - 6 = (2/9)(x - 9)
---> 9(y - 6) = 2(x - 9)
---> 9y - 54 = 2x - 18
---> 9y = 2x + 36
---> y = (2/9)x + 4
This equation has a slope of 2/9 and a y-intercept of 4.
