What is an equation of the line that is perpendicular to y=−3/4x+6 and passes through the point (3, 9) ?

Mathematics

2 answers:

irga5000 [103]3 years ago

5 0

Two straight lines perpendicular to each other, the slope of which is negative reciprocal.

y=-4/3x+b

The known points are put into the linear equation

y=-4+b

b=13

y=-4/3x+13

Dimas [21]3 years ago

4 0

First, put the equation of the line given into slope-intercept form by solving for y. You get y = 2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6.

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Temka [501]

Looking at the graph, we can say that:

- It opens downward and has a maximum of 0.

- The axis of symmetry passes through the vertex (the maximum value in this case). So, the x-coordinate of the vertex is 4, and the axis of symmetry is:

$x=4$

- We conclude that the coordinates of the vertex are:

$\text{Vertex }=(4,0)$

- The x-intercepts are defined as those points whose y-coordinate is 0. Similarly, the y-intercepts are those points of x-coordinate equal to 0. Looking at the graph, the vertex itself is the x-intercept, and y = -8 is the y-intercept.