Answer :
To find the equation of the line that passes through 2 points, we have to find the slope and the y-intercept
The form of the equation is y = mx + b
m is the slope
b is the y-intercept
The rule of the slope is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Since the line passes through points (0, 7) and (3, 10), then
x1 = 0 and x2 = 3
y1 = 7 and y2 = 10
[tex]\begin{gathered} m=\frac{10-7}{3-0} \\ m=\frac{3}{3} \\ m=1 \end{gathered}[/tex]Substitute m in the rule of the equation
[tex]\begin{gathered} y=1(x)+b \\ y=x+b \end{gathered}[/tex]Since b is the y-intercept (value y at x = 0)
Since the line passes through the point (0, 7), then
b = 7
The equation of the line is
[tex]y=x+7[/tex]The answer is C
