Question

Write an equation in​ slope-intercept form of the line satisfying the given conditions.
Through ​(7​,11​), parallel to negative 9 x minus 4 y equals negative 95

Answer 1

To find the equation of the line parallel to the given line, we need to find the slope of the given line and then use the point-slope form.

First, let's rewrite the given equation in slope-intercept form:
-9x - 4y = -95
-4y = 9x - 95
y = (-9/4)x + 23.75

From the equation, we can see that the slope of the given line is -9/4.

Since the line we want is parallel to this line, it will have the same slope of -9/4.

Now, let's use the point-slope form with the point (7, 11) and the slope -9/4:
y - y₁ = m(x - x₁)
y - 11 = (-9/4)(x - 7)

Now, let's simplify the equation:
y - 11 = (-9/4)x + 63/4

Finally, let's rewrite the equation in slope-intercept form:
y = (-9/4)x + 63/4 + 11
y = (-9/4)x + 63/4 + 44/4
y = (-9/4)x + 107/4

Therefore, the equation of the line satisfying the given conditions is y = (-9/4)x + 107/4.