The equation of the line in slope-intercept form is:
y = x - 3
Explanation:Given the points (3, 0) and (5, 2)
The equation of a line in slope-intercept form is:
y = mx + b .....................................................(1)
Where m is the slope and b the y-intercept
To obtain the slope, we use the formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ =\frac{2-0}{5-3}=\frac{2}{2}=1 \end{gathered}[/tex]Using the obtained m = 1, the equation now becomes
y = (1)x + b
OR
y = x + b ............................................................(2)
Using either of the given points (say (3, 0)), we have x = 3 and y = 0.
Substitute these into equation (2), we have:
0 = 3 + b
b = 0 - 3 = -3
Therefore, the required equation of the line in slope-intercept form is:
y = x - 3
