Final answer:
The line perpendicular to y = 2x – 5 passing through (�9, 6) has a slope of -1/2. Using the point-slope form, the equation is y - 6 = -1/2(x + 9), which simplifies to y = -1/2x + 1.5 in slope-intercept form.
Step-by-step explanation:
To find the equation of the line that is perpendicular to y = 2x – 5 and passes through the point (–9, 6), first, we need to understand the relationship between the slopes of perpendicular lines. If a line has a slope m, then any line perpendicular to it will have a slope that is the negative reciprocal, –(1/m). The given line y = 2x – 5 has a slope of 2, so our perpendicular line must have a slope of –(1/2).
We can use the point-slope form equation of line, which is y – y₁ = m(x – x₁), where (x₁, y₁) is a point on the line (in this case, –9, 6) and m is the slope.
Plugging in our values, we get:
y – 6 = –½(x + 9)
This is the perpendicular line's equation in point-slope form. To convert it to slope-intercept form y = mx + b, we distribute the –½ and solve for y:
y – 6 = –½x – –½(9)
y = –½x + –4.5 + 6
y = –½x + 1.5
Therefore, the equation of our perpendicular line in slope-intercept form is y = –½x + 1.5.