Answer :
Given the points:
(x1, y1) ==> (4, 2)
(x2, y2) ==> (5, 4)
Let's find the line passing through the points in slope-intercept form.
Apply the slope-intercept form of a linear equation:
y = mx + b
Where m is the slope and b represents the y-intercept.
To find the slope, m, apply the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Thus, we have:
[tex]\begin{gathered} m=\frac{4-2}{5-4} \\ \\ m=\frac{2}{1} \\ \\ m=2 \end{gathered}[/tex]The slope, m is 2.
We have:
[tex]y=2x+b[/tex]Plug in the values of one point for x and y to solve for b.
Take the first point:
(x, y) ==> (4, 2):
[tex]\begin{gathered} 2=2(4)+b \\ \\ 2=8+b \\ \\ Subtract\text{ 8 from both sides:} \\ 2-8=8-8+b \\ \\ -6=b \\ \\ b=-6 \end{gathered}[/tex]Therefore, the y-intercept, b, = -6.
The equation of the line passing through the points in slope-intercept form is:
[tex]y=2x-6[/tex]• ANSWER:
[tex]y=2x-6[/tex]