Answer:
Therefore, the equation in slope-intercept form for line B is y = (-3/2)x - 9
Explanation:
To find the equation of line B, which is perpendicular to line A, we need to first determine the slope of line A.
The slope of line A can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
Given that line A passes through (-6, -7) and has a y-intercept of -3, we can use the y-intercept to find a second point on line A.
Since the y-intercept is where the line crosses the y-axis, its coordinates are (0, -3).
Using the coordinates (-6, -7) and (0, -3), we can calculate the slope of line A as follows:
slope = (-3 - (-7)) / (0 - (-6))
slope = 4 / 6
slope = 2/3
Since line B is perpendicular to line A, its slope is the negative reciprocal of line A's slope.
The negative reciprocal of 2/3 is -3/2.
Now, we have the slope (-3/2) of line B and a point it passes through, (-8, 3).
To find the equation of line B in slope-intercept form (y = mx + b), we can substitute the slope and the coordinates of the point into the equation and solve for b.
Using the point-slope form of a linear equation:
y - y1 = m(x - x1)
We substitute the values:
y - 3 = (-3/2)(x - (-8))
Next, we simplify and distribute:
y - 3 = (-3/2)(x + 8)
y - 3 = (-3/2)x - 12
Finally, we isolate y to get the equation in slope-intercept form:
y = (-3/2)x - 12 + 3
y = (-3/2)x - 9
Therefore, the equation in slope-intercept form for line B is y = (-3/2)x - 9.