Catherine saved some money and plans to add the same amount of each week to her savings account. the table represents the number of weeks that she will save, x, and the total amount of money that she will have in her account, y.

which linear equation represents Catherine's situation?
a. y=1/6x + 70
b. y=6x +50
c. y=1/9x +104
d. y=11x +116

We will represent the amount of money saved by Catherine in her savings account in slope-intercept form of equation: [tex]y=mx+b[/tex], where m represents slope and b represents y-intercept.

Let us find the slope of line using slope formula.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where,

[tex]y_2-y_1[/tex] = Difference between two y-coordinates.

[tex]x_2-x_1[/tex] = Difference between same x-coordinates of two y-coordinates.

Upon substituting coordinates of points (4,74) and (11,116) in slope formula we will get,

[tex]m=\frac{116-74}{11-4}[/tex]

[tex]m=\frac{42}{7}[/tex]

[tex]m=6[/tex]

Let us substitute [tex]m=6[/tex] and coordinates of point (4,74) in slope intercept form of equation to find y-intercept or initial amount of money,

[tex]74=6*4+b[/tex]

[tex]74=24+b[/tex]

[tex]74-24=24-24+b[/tex]

[tex]50=b[/tex]

Upon substituting [tex]b=50[/tex] and [tex]m=6[/tex] in slope-intercept form of equation we will get,

[tex]y=6x+50[/tex]

Therefore, the equation [tex]y=6x+50[/tex] represents the total amount (y) in Catherine's account after x weeks and option b is the correct choice.