Question

(-2, 8), (3, 18); b = 6

Slope =
A) 2
B) 3
C) 4
D) 6
y-intercept =
A) -4
B) 4
C) 6
D) 8
Equation in slope-intercept form:
A) y = 2x + 4
B) y = 3x + 6
C) y = 4x + 8
D) y = 6x - 4

Answer 1

The slope of the line through the points (-2, 8) and (3, 18) is 2, and the slope-intercept form of the equation, given the y-intercept as 6, is y = 2x + 6.

Step-by-step explanation:

To determine the slope and y-intercept of the line passing through the points (-2, 8) and (3, 18) we can use the formula for slope, which is Δy / Δx (change in y over change in x). The slope (Δy / Δx) is calculated as (18 - 8) / (3 - (-2)) = 10 / 5 = 2. This makes our slope 2.

Since the y-intercept is the value of y when x=0, we can plug the slope into one of the point's coordinates and solve for y-intercept (b). If we use point (3,18) and the slope-intercept form, y = mx + b, we get 18 = 2(3) + b. Solving for b, we get b = 18 - 6 = 12. However, we are given that b = 6, which suggests a discrepancy and that possibly, the y-intercept provided is incorrect based on the given points.

Ignoring the discrepancy and using the understood formula of y-intercept as the given 'b' for the final equation y = mx + b, our linear equation in slope-intercept form is y = 2x + 6, corresponding to option B for the slope and option C for the y-intercept.