Question

For the straight line defined by the points (3,57) and (5,87), determine the slope ( m ) and y-intercept ( ???? ). Do not round the answers.

Answer 1

The slope of the line is 15 and the y-intercept is 12.

Step-by-step explanation:

To determine the slope of a straight line, we use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of any two points on the line. For the given line defined by the points (3,57) and (5,87), the slope can be calculated as follows:

m = (87 - 57) / (5 - 3) = 30 / 2 = 15.

The y-intercept of a straight line is the point where the line intersects the y-axis. To find the y-intercept, we can substitute the coordinates of one of the points into the equation y = mx + b and solve for b. Let's substitute the coordinates of (3,57) into the equation:

57 = 15(3) + b

57 = 45 + b

b = 57 - 45 = 12.

Therefore, the slope (m) of the line is 15 and the y-intercept (b) is 12.

Answer 2

Answer: The slope of the line is 15 and y-intercept is 12.

Step-by-step explanation: We are given to find the slope and y-intercept of the straight line defined by the points (3, 57) and (5, 87).

We know that

the slope of a line passing through the points (3, 57) and (5, 87) is given by

`m=(87-57)/(5-3)=(30)/(2)=15.`

Since the straight line passes through the point (3, 57), so its equation will be

`y-57=m(x-3)\\\\\Rightarrow y-57=15(x-3)\\\\\Rightarrow y-57=15x-45\\\\\Rightarrow y=15x-45+57\\\\\Rightarrow y=15x+12.`

So, the required equation of the straight line is
`y=15x+12.`

Thus, the slope of the line is 15 and y-intercept is 12.