Given the points:
(x1, y1) ==> (1, 1)
(x2, y2) ==> (3, 7)
To find an equation of the line that goes through the points, first find the slope using the slope formula below:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Substitue values into the formula and solve for the slope, m:
[tex]\begin{gathered} m=\frac{7-1}{3-1} \\ \\ m=\frac{6}{2} \\ \\ m=3 \end{gathered}[/tex]The slope of the line, m is = 3.
Now, use the point slope form:
(y - y1) = m(x - x1)
Substitute 1 for y1, 1 for x1, and 3 for m:
(y - 1) = 3(x - 1)
Let's rewrite the equation to slope intercept form: y = mx + b
Where m is the slope and b is the y-intercept
y - 1 = 3(x) + 3(-1)
y - 1 = 3x - 3
Add 1 to both sides:
y - 1 + 1 = 3x - 3 + 1
y + 0 = 3x - 2
y = 3x - 2
Therefore, the equation of the line in slope intercept form is:
y = 3x - 2
ANSWER:
y = 3x - 2
