Answer:
To find the slope-intercept form of the line that passes through the points (−2, 6) and (−1, 18), we can use the slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept.
First, we need to find the slope of the line. The slope of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Substituting the coordinates of the points given in the problem, we have:
m = (18 - 6) / (−1 - (−2)) = 12 / 3 = 4
Next, we need to find the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis, which has an x-coordinate of 0. Substituting the slope and the coordinates of one of the points given in the problem, we can solve for b:
y = mx + b
6 = 4 * (−2) + b
6 = −8 + b
b = 6 + 8 = 14
Therefore, the slope-intercept form of the line that passes through the points (−2, 6) and (−1, 18) is y = 4x + 14.
Explanation: