Question

A graph is given below. Answer the following questions based off the graph:

Answer 1

(a) The slope of the graph is $\frac{2}{5}$

(b) The equation of the line in point-slope form is y - 1 = $\frac{2}{5}$ (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 $(x_{1},y_{1})$ and $(x_{2},y_{2})$

is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The equation of a line in a point-slope form is:

$y-y_{1}=m(x-x_{1})$

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)

∵ $(x_{1},y_{1})$ = (-5 , 0)

∵ $(x_{2},y_{2})$ = (0 , 2)

∴ $m=\frac{(2-0)}{(0--5)}=\frac{2}{5}$

The slope of the graph is $\frac{2}{5}$

(b)

∵ Point (-2.5 , 1) lies on the line

∴ $(x_{1},y_{1})$ = (-2.5 , 1)

∵ The point-slope form is ⇒ $y-y_{1}=m(x-x_{1})$

∵ m = $\frac{2}{5}$

- Substitute the coordinates of the point and the slope in the equation

∴ y - 1 = $\frac{2}{5}$ (x - -2.5)

∴ y - 1 = $\frac{2}{5}$ (x + 2.5)

The equation of the line in point-slope form is y - 1 = $\frac{2}{5}$ (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 = $\frac{2}{5}$ (x + 2.5)

∴ y - 1 = $\frac{2}{5}$ (0 + 2.5)

∴ y - 1 = $\frac{2}{5}$ (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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