Question

The following diagram shows part of the graph off with x-intercept (5,0) and y-intercept (0,8).

Find the y-intercept of the graph of f(x) + 3.

Answer 1

Explanation:

By question , it's given that the X intercept is (5,0) and the y intercept is (0,8) . And we need to find the y-intercept of the graph of f(x) + 3 . For that , firstly let's find out the equation of the line.

• We can use here two point form of the line .So that , the equation would be ,

`\sf\implies y- y_1 = \bigg((y_2-y_1)/(x_2-x_1)\bigg) ( x - x_1) \\\\\sf\implies y - 0 = \bigg((0-8)/(5-0)\bigg)( x - 5 ) \\\\\sf\implies y = (-8)/(5)( x - 5 ) \\\\\sf\implies 5y = -8x +40 \\\\\sf\implies 8x + 5y - 40 = 0`

Let us say that this is f(x) :-

`\\\\\sf\implies f(x) = 8x + 5y - 40 \\\\\sf\implies \boxed{\sf\red{ f(x)+3 = 8x +5y -37 }}`

Plot its graph :-

We can either convert it into intercept form but plotting a graph can also be done to find y intercept .

`\implies \boxed{\pink{\sf y - intercept = 7.4}}`

Refer to attachment for graph .

Hence the y Intercept is 7.4 .