Question

How do I write the equation in slope intercept form by simply identifying its slope and y intercept

Answer 1

From the graph given,

The following points can be picked

Where x = 0, y = -5, i.e

`(x_1,y_1)\Rightarrow(0,-5)`

Where x = 2, y = 3, i.e

`(x_2,y_2)\Rightarrow(2,3)`

To find the equation of a straight line, the formula is

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

Substitute the points into the formula above to find the equation of the graph

`\begin{gathered} (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \\ \frac{y-(-5)_{}}{x-0}=(3-(-5))/(2-0) \\ (y+5)/(x)=(3+5)/(2) \\ (y+5)/(x)=(8)/(2) \\ (y+5)/(x)=(4)/(1) \\ \text{Crossmultiply} \\ 1(y+5)=4* x \\ y+5=4x \\ y=4x-5 \end{gathered}`

The equation of the line is y = 4x -5 in the slope-intercept form

The general form of the equation of a straight line is

`\begin{gathered} y=mx+b \\ \text{Where m is the slope and b is the y-intercept} \end{gathered}`

Relating both equations,

The slope, m, is 4 and the y-intercept, b, is -5

Hence, the answers are m = 4 and b = -5

`\begin{gathered} m=4\text{ } \\ b=-5 \end{gathered}`