A linear function has a slope of 2 and passes through the point (1, 3). What is its y-intercept?

A linear function has a slope of 2 and passes through the point (1, 3). What is its y-intercept?

• A. 1
• B. 2
• C. 3
• D. 4

Answer: (B)

To find the y-intercept of a linear function given its slope and a point through which it passes, we can use the point-slope form of a linear equation. The general form of a linear equation is given by: \[ y = mx + b \] where \( m \) is the slope, \( b \) is the y-intercept, and \( (x, y) \) is a point on the line. In this case, the slope \( m \) is specified as 2, and the line passes through the point (1, 3), where \( x = 1 \) and \( y = 3 \). Substituting these values into the equation gives: \[ 3 = 2(1) + b \] This simplifies to: \[ 3 = 2 + b \] Next, we solve for \( b \) (the y-intercept): \[ b = 3 - 2 \] \[ b = 1 \] Thus, the y-intercept of the linear function is 1. Therefore, the correct answer identifies the y-intercept as 1. Choosing option B, which suggests the y-intercept is 2, does not align with the calculation

To find the y-intercept of a linear function given its slope and a point through which it passes, we can use the point-slope form of a linear equation. The general form of a linear equation is given by:

[ y = mx + b ]

where ( m ) is the slope, ( b ) is the y-intercept, and ( (x, y) ) is a point on the line.

In this case, the slope ( m ) is specified as 2, and the line passes through the point (1, 3), where ( x = 1 ) and ( y = 3 ). Substituting these values into the equation gives:

[ 3 = 2(1) + b ]

This simplifies to:

[ 3 = 2 + b ]

Next, we solve for ( b ) (the y-intercept):

[ b = 3 - 2 ]

[ b = 1 ]

Thus, the y-intercept of the linear function is 1. Therefore, the correct answer identifies the y-intercept as 1. Choosing option B, which suggests the y-intercept is 2, does not align with the calculation