Answer:
b = -9
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points M(4, 3) and N(7, 12). Substitute:
[tex]m=\dfrac{12-3}{7-4}=\dfrac{9}{3}=3[/tex]
Therefore we have the equation:
[tex]y=3x+b[/tex]
Put the coordinates of the point M to the equation:
[tex]3=3(4)+b[/tex]
[tex]3=12+b[/tex] subtract 12 from both sides
[tex]-9=b[/tex]
