A line has slope 4/3.Through which two points could this line pass?

2.a

To find two points through which a line with a given slope passes, we need to consider the slope-intercept form of a linear equation: y = mx + b, where m represents the slope, and b represents the y-intercept.

Given that the slope of the line is 4/3, we can substitute this value into the slope-intercept equation: y = (4/3)x + b.

To find the intercept (b), we need additional information or constraints. If we have a specific point that the line passes through, we can substitute the coordinates of that point into the equation to solve for b.

However, if no additional information is provided, we can choose any value for b, and it will yield a valid equation for a line with a slope of 4/3. This means that there are infinitely many points through which the line can pass.

Let's assume a value for b, say b = 0. Plugging this into the equation, we have y = (4/3)x + 0, which simplifies to y = (4/3)x. Now, we can choose any x value and calculate the corresponding y value to get two points on the line.

For example, if we choose x = 3, we can calculate y: y = (4/3)(3) = 4. Therefore, one point on the line is (3, 4).

Similarly, if we choose x = 6, we get y: y = (4/3)(6) = 8. The second point on the line is (6, 8).

Hence, two points through which the line with a slope of 4/3 can pass are (3, 4) and (6, 8).