Final answer:
The equation in slope-intercept form for the line that passes through the point (-3, 5) and is perpendicular to the given equation 5x - 6y = 9 is y = (-6/5)x + 7/5.
Step-by-step explanation:
To find an equation in slope-intercept form for the line that is perpendicular to the graph of the given equation, we need to find the slope of the given equation first. The given equation is 5x - 6y = 9. To write it in slope-intercept form, we solve for y:
5x - 6y = 9
-6y = -5x + 9
y = (5/6)x - (9/6)
Therefore, the slope of the given equation is 5/6.
Since the line we are looking for is perpendicular to the given equation, its slope will be the negative reciprocal of 5/6. The negative reciprocal of 5/6 is -6/5.
Now we have the slope of the line we are looking for (-6/5) and a point it passes through (-3, 5). We can use the point-slope form of the equation to write the equation in slope-intercept form:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
Plugging in the values, we have:
y - 5 = (-6/5)(x + 3)
y - 5 = (-6/5)x - 18/5
y = (-6/5)x - 18/5 + 25/5
y = (-6/5)x + 7/5
Therefore, the equation in slope-intercept form for the line that passes through the point (-3, 5) and is perpendicular to the graph of the given equation is y = (-6/5)x + 7/5.