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Answer: the x-intercept is (-10,0), the y-intercept is (0,45/2)
Explanation:
First, we need to determine the function describing the line.
From the table, it is obvious that the y values increase by 9 every increase of 4 of the x values. So, the slope is 9/4 and the function looks like this:
[tex]y = m x+ b = \frac{9}{4}x + b[/tex]
with the y-intercept (or bias) b still unknown. This can be determined by using one of the point from the table, like so:
[tex]-18 = \frac{9}{4}\cdot 2+b\\\implies b = -18 -\frac{9}{2}=\frac{45}{2}\\y = \frac{9}{4}x+\frac{45}{2}[/tex]
The above function form makes it easy to read off the y-intercept, which is (0,45/2) or (0,22.5). The x-intercept is obtained by setting y = 0 and solving for x:
[tex]y = \frac{9}{4}x+\frac{45}{2}\\0 = \frac{9}{4}x+\frac{45}{2}\\-\frac{45}{2}=\frac{9}{4}x\\x = -10[/tex]
The x-intercept is (-10,0)
Answer:
y-intercept = (0,-27/2); x-intercept = (-6,0)
Explanation:
The equation for a straight line is
y = mx + b
Step 1. Calculate the slope
m = (y₂ - y₁)/(x₂ - x₁)
y₂ = - 36; y₁ = -18
x₂ = 10; x₁ = 2
m = [- 36 – (-18)]/(10-2)
m = (-36 + 18)/8
m = -18/8
m = -9/4
===== ==========
Step 2. Calculate the y-intercept
y = -(9/4)x + b
When x = 2, y = -18 Insert the values
-18 = -(9/4)×2 + b
-18 = -9/2 +b
-18 + 9/2 = b
b = (-36 + 9)/2
b = -27/2
The y-intercept is at (0, -27/2).
===== ==========
Step 3. Calculate the x-intercept
y = -(9/4)x – 27/2 Set y = 0
0 = -(9/4)x – 27/2 Multiply each side by -1
0 = (9/4)x + 27/2 Multiply each side by 4
0 = 9x + 54 Divide each side by 9
0 = x + 6 Subtract 6 from each side
x = -6
The x-intercept is at (-6, 0).
The graph shows the x-intercept at (-6,0) and the y-intercept at (0, -27/2).