Question

Write the equation of a line in slope-intercept form that contains the point (3, 4) with a slope of 2/3.

A) y = (2/3)x + 4
B) y = (3/2)x + 4
C) y = (2/3)x - 3
D) y = (3/2)x - 3

Answer 1

The equation of a line with a slope of 2/3 that contains the point (3, 4) in slope-intercept form is y = (2/3)x + 2, which is not presented in the options given. To find this, plug the slope and point into the slope-intercept form equation, y = mx + b, and solve for b.

Step-by-step explanation:

To write the equation of a line in slope-intercept form that contains the point (3, 4) with a slope of 2/3, you need to use the formula y = mx + b, where m is the slope and b is the y-intercept. Starting with the slope of 2/3, we can plug in the point (3, 4) into the equation to solve for b.

The steps are as follows:

1. Start with the slope-intercept form: y = mx + b.
2. Plug in the slope (m = 2/3) and the coordinates of the given point (x = 3, y = 4): 4 = (2/3)*3 + b.
3. Multiply 2/3 by 3 to get 2: 4 = 2 + b.
4. Subtract 2 from both sides to solve for b: b = 4 - 2, so b = 2.
5. The equation of the line is therefore: y = (2/3)x + 2.

None of the options provided (A, B, C, D) match the correct equation. Therefore, it seems there might be a typo in the question or the provided options. The correct answer should be y = (2/3)x + 2, which is not listed among the options given to us.