Question

The equation of line j is y-3 =– 1/8 (x–8). Line k includes the point (1,7) and is perpendicular to line j. What is the equation of line k?

a) y=8(x−1)−7
b) y=8(x−1)-3
c) y=−8(x−1)+7
d) y=−8(x−1)-3

Answer 1

The equation of line k, perpendicular to line j and passing through the point (1,7), is y = 8(x - 1) + 7. Hence, option a) is correct.

Step-by-step explanation:

Given that line j has the equation y-3 = – 1/8 (x–8), we can determine its slope and y-intercept. The slope of line j is -1/8, which means that for every 1 unit increase in x, there is a decrease of 1/8 unit in y. The y-intercept is 3.

Since line k is perpendicular to line j, the slopes of the two lines are negative reciprocals of each other. Hence, the slope of line k is 8. We also know that line k passes through the point (1,7). Using the point-slope form, we can find the equation of line k: y - y1 = m(x - x1), where (x1, y1) is the given point on the line and m is the slope. Plugging in the values, we get y - 7 = 8(x - 1), which simplifies to y = 8(x - 1) + 7.

Therefore, the equation of line k is y = 8(x - 1) + 7, which corresponds to option a).