Question

Write an equation of a line given two points. Identify the slope and the y-intercept separately.

(1) (-1,-9), (2,0)
a) y = 3x - 6; Slope: 3, Y-Intercept: -6
b) y = -3x - 6; Slope: -3, Y-Intercept: -6
c) y = 3x + 6; Slope: 3, Y-Intercept: 6
d) y = -3x + 6; Slope: -3, Y-Intercept: 6

Answer 1

To write an equation of a line given two points, we can use the slope-intercept form: y = mx + b. Given the points (-1, -9) and (2, 0), we can calculate the slope using the formula: slope = (y2 - y1) / (x2 - x1). Using one of the points, we can substitute it into the equation y = mx + b to find the y-intercept.

Step-by-step explanation:

To write an equation of a line given two points, we can use the slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept.

Given the points (-1, -9) and (2, 0), we can calculate the slope using the formula: slope = Δy / Δx = (y2 - y1) / (x2 - x1).

Plugging the values into the formula, we have slope = (0 - (-9)) / (2 - (-1)) = 9 / 3 = 3.

Now that we have the slope, we can substitute one of the points into the equation y = mx + b and solve for b. Using the point (-1, -9), we have -9 = 3(-1) + b. Solving for b gives us b = -9 + 3 = -6.

Therefore, the equation of the line is y = 3x - 6, where the slope is 3 and the y-intercept is -6.