Question

How would you find the slope and equation for this?

Answer 1

`y=-(1)/(2)x+1`

Explanation:

Given the line with the two points:

`\begin{gathered} (x_1,y_1)=(0,1) \\ (x_2,y_2)=(4,-1) \end{gathered}`

We want to find the equation of the line in the slope-intercept form.

The slope-intercept form is given as:

`y=mx+b`

Step 1: Determine the slope of the line.

`\text{Slope, }m=(y_2-y_1)/(x_2-x_1)`

Substitute the given values:

`\text{Slope, }m=(-1-1)/(4-0)=-(2)/(4)=-(1)/(2)`

Step 2: Determine the y-intercept.

The line crosses the y-axis at y=1, therefore, the y-intercept, b = 1.

Step 3: Substitute these values into the slope-intercept form.

`y=-(1)/(2)x+1`

The equation of the line is:

`y=-(1)/(2)x+1`