(a) The slope of the graph is
(b) The equation of the line in point-slope form is y - 1 = (x + 2.5)
(c) The y-intercept of the graph is (0 , 2)
(d) The y-intercept is correct
(e) We substitute x by zero because the line intersects y-axis at a point
its x-coordinate must be zero. Then we calculate the value of
y-coordinate when x = 0. The y-coordinate = 2, so the
y-intercept is (0 , 2)
Step-by-step explanation:
The slope of a line whose endpoints are and
is
The equation of a line in a point-slope form is:
From the graph:
1. The line passes through points (-5 , 0) and (0 , 2)
2. Substitute these points in the rule of the slope to find it
3. Writ the equation of the line in the form of point-slope
(a)
∵ = (-5 , 0)
∵ = (0 , 2)
∴
The slope of the graph is
(b)
∵ Point (-2.5 , 1) lies on the line
∴ = (-2.5 , 1)
∵ The point-slope form is ⇒
∵ m =
- Substitute the coordinates of the point and the slope in the equation
∴ y - 1 = (x - -2.5)
∴ y - 1 = (x + 2.5)
The equation of the line in point-slope form is y - 1 = (x + 2.5)
(c)
When the line intersects the y-axis at point (0 , b), then b is the
y-intercept
∵ The line intersects y-axis at point (0 , 2)
∴ The y-intercept is (0 , 2)
The y-intercept of the graph is (0 , 2)
(d)
Let us substitute x in the equation by zero
∵ x = 0
∵ The point slope form of the equation is y - 1 = (x + 2.5)
∴ y - 1 = (0 + 2.5)
∴ y - 1 = (2.5)
∴ y - 1 = 1
- Add 1 to both sides
∴ y = 2
- When x = 0 then y = 2
∴ Point (0 , 2) is the y-intercept
The y-intercept is correct
(e)
We substitute x by zero because the line intersects y-axis at a point its
x-coordinate must be zero
Then we calculate the value of y-coordinate when x = 0
The y-coordinate = 2, so the y intercept is (0 , 2)
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