Question

Whats the slope-intercept form of the equation of the lined graph in this figure?

Answer 1

`y=(3)/(5)x+1`

Explanation:

Given:

A line with two points on it. The points are:

`(x_1,y_1)=(-5,-2)\\\\(x_2,y_2)=(5,4)`

The slope-intercept form of the equation of a line is given as:

`y=mx+b`

Where 'm' is the slope of the line and 'b' is the y-intercept.

The slope of a line with two points
`(x_1,y_1)\ and\ (x_2,y_2)` on it is given as:

`m=(y_2-y_1)/(x_2-x_1)`

Plug in the given values and solve for 'm'. This gives,

`m=(4-(-2))/(5-(-5))\\\\ m=(4+2)/(5+5)\\\\m=(6)/(10)\\\\m=(3)/(5)`

Now, y-intercept is the value of 'y' where 'x' is 0 or the point where the line crosses the y axis.

From the graph, the line cuts the y-axis at the point (0, 1).

Therefore, the y-intercept is,
`b=1`

Hence, the equation of the line is given as:

`y=mx+b\\\\y=(3)/(5)x+1`