If a ship's path is mapped on a coordinate grid, it follows a straight-line path of slope 4 and passes through point (1, 2).
Part A: Write the equation of the ship’s path in slope-intercept form. (2 points)
Part B: A second ship follows a straight line, with the equation x + 4y − 20 = 0. Are these two ships sailing perpendicular to each other? Justify your answer. (2 points)
We want the equation of the line with a slope of 4 that passes through the point (1, 2)
We know a point (1, 2) and we know the slope 4
So we can write the equation in point-slope form.
y - 2 = 4(x - 1) To get this into slope-intercept form, distribute the 4 .
y - 2 = 4x - 4 Add 2 to both sides.
y = 4x - 2
Is the line x + 4y - 20 = 0 perpendicular to the line y = 4x - 2 ?
The slope of the line y = 4x - 2 is 4.
To find the slope of the line x + 4y - 20 = 0 , let's get the equation into slope-intercept form.
x + 4y - 20 = 0 Add 20 to both sides.
x + 4y = 20 Subtract x from both sides.
4y = -x + 20 Divide both sides by 4 .
y = -\(\frac14\)x + 5 Now we can see that the slope of this line is -\(\frac14\) .
Since -\(\frac14\) is the negative reciprocal of 4 , these lines are perpendicular.
Yes, the two ships are sailing perpendicular to each other.