Answer :
Answer:
[tex]y=\dfrac{1}{2}x+5[/tex]
Step-by-step explanation:
Slope - Intercept Form
Linear functions and equations can be written in slope-intercept form which is the formal name of y = mx + b, where m is the slope and b is the y-intercept of the line.
To find m using 2 points on the line, we use this formula:
[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex],
where the subscripts 1 and 2 indicates which coordinate pair the value originates from.
If we're given a solution to the line then we can plug its x and y value into the equation and rearrange to find the b value.
Solving the Problem
We're given two points, so we plug them into the slope formula.
Let [tex](x_2,y_2)=(6,8)[/tex] and [tex](x_1,y-1)=(-4,3)[/tex],
[tex]\dfrac{8-3}{6-(-4)} =\dfrac{5}{10} =\dfrac{1}{2}[/tex].
Plugging the m value into the slope-intercept format we have,
[tex]y=\dfrac{1}{2}x+b[/tex].
Now we can plug either (-4,3) or (6,8), we'll plug in (6,8) for simplicity.
[tex]8=\dfrac{1}{2}(6)+b\\\\[/tex]
[tex]8=3+b\\\Longrightarrow 5 = b[/tex]
So, the equation of the line is [tex]y=\dfrac{1}{2}x+5[/tex].
