Answer:
[tex]y=-\frac{1}{2}x+1[/tex]
Explanation:
Given the line with the two points:
[tex]\begin{gathered} (x_1,y_1)=(0,1) \\ (x_2,y_2)=(4,-1) \end{gathered}[/tex]
We want to find the equation of the line in the slope-intercept form.
The slope-intercept form is given as:
[tex]y=mx+b[/tex]
Step 1: Determine the slope of the line.
[tex]\text{Slope, }m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given values:
[tex]\text{Slope, }m=\frac{-1-1}{4-0}=-\frac{2}{4}=-\frac{1}{2}[/tex]
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.
[tex]y=-\frac{1}{2}x+1[/tex]
The equation of the line is:
[tex]y=-\frac{1}{2}x+1[/tex]
