Question

"A line goes through the point (2, 4) and has a slope of 3 2. Which of the following points is also on the line? Circle all that apply.

A. (1, 1) B. (3, 7)
C. (0, 2) D. (4, 7)
E. (0, 1) F. (0, 0)

Answer 1

To determine the points that are also on the given line, we can use the point-slope form of a linear equation, y - y1 = m(x - x1). By substituting the given point and slope into the equation, we can find the equation of the line. Then, by substituting the x and y values of each point option into the equation, we can determine which points satisfy the equation and are therefore on the line.

Step-by-step explanation:

To determine which points are also on the line, we can use the point-slope form of a linear equation. The point-slope form is given as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Using the given point (2, 4) and slope 3/2, we have y - 4 = (3/2)(x - 2). Simplifying, we get y = (3/2)x - 5.

Now we can substitute the x and y values of each point option and check if they satisfy the equation y = (3/2)x - 5.

When substituting the values from each option into the equation, we find that points B. (3, 7) and F. (0, 0) satisfy the equation. So, options B and F are the correct answers.