Question

How to find Y intercept of the line passing through the points

Answer 1

Y-intercept: (0, -3)

Explanation:

Given the two points, (6, 5) and (3, 1):

We can find the y-intercept by using the slope-intercept form, y = mx + b. However, the first step that we must do is to solve for the slope.

Slope

We must first solve for the slope of the line using the following formula:

`\displaystyle\mathsf{Slope\:(m) =\:(y_2 - y_1)/(x_2 - x_1)}`

Let (x₁, y₁) = (3, 1)

(x₂, y₂) = (6, 5)

`\displaystyle\mathsf{Slope\:(m) =\:(y_2 - y_1)/(x_2 - x_1)}`

`\displaystyle\mathsf{Slope\:(m) =\:(5 - 1)/(6 - 3)\:=\:(4)/(3)}`

Hence, the slope of the line is:
`\sf{m\:=(4)/(3)}` .

Y-intercept:

Next, we must determine the y-intercept, which is the point on the graph where it crosses the y-axis, with coordinates of (0, b ).

In order to find the y-intercept, use one of the given points, (6, 5), and the slope,
`\sf{m\:=(4)/(3)}`, and substitute these values into the slope-intercept form and solve for the value of b:

y = mx + b

`\displaystyle\mathsf{5\:=\:(4)/(3)(6)\:+\:b }`

5 = 8 + b

Subtract 8 from both sides to isolate b:

5 - 8 = 8 - 8 + b

-3 = b

Therefore, the y-intercept is (0, -3), where b = -3.