For the straight line defined by the points (1, 57) and (3, 91), determine the slope and y-intercept. Do not round the answers.

To determine the slope and y-intercept of the straight line defined by the points (1, 57) and (3, 91), we start with the formula for the slope (m) of a line given two points (x₁, y₁) and (x₂, y₂):

m = (y₂ – y₁) / (x₂ – x₁)

Substituting our points into the formula:

• (x₁, y₁) = (1, 57)
• (x₂, y₂) = (3, 91)

So:

m = (91 – 57) / (3 – 1)

Calculating the differences:

m = 34 / 2 = 17

Now that we have the slope, we can find the y-intercept (b) using the slope-intercept form of the line, which is:

y = mx + b

We can use one of the points to solve for b. Let’s use the point (1, 57):

57 = 17(1) + b

Solving for b:

57 = 17 + b

b = 57 – 17

b = 40

In summary, the slope of the line is 17 and the y-intercept is 40.