Answer:
Write the equation of a line that is perpendicular to the given line and that passes through the given point. 2x + 4y = –6; (2,
1 answer:
First we have to find the slope of the given line. We do that by puttiing the equation into slope-interept form. or solving it for y (same thing). 2x + 4y = -6. We move the 2x over by subtraction to get 4y = -2x - 6. Divide both sides by 4 to get the slope-intercept form we are seeking. . The slope that is perpendicular to that slope of -1/2 is the opposite reciprocal. Therefore, the perpendicular slope is a positive 2/1 or just 2. If this new line goes through the point (2, 5), it goes through the x value of 2 and the y value of 5. We will use those values along with the slope of 2 to solve for b in our slope-intercept equation. That looks like this:
and b = 1. That means our new equation, the one that is perpendicular to the given line, has an equation of y = 2x + 1.
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The coordinate set (0, 0), (2, 1), (4, 2), (6, 3) represents a straight line. Since the first point is (0, 0) the y-intercept is 0. Now, lets solve for the slope (we can use any of the four points to solve).
Slope formula: y2-y1/x2-x1
= 2-1/4-1
= 1/2
Now that we know what the slope is, we can write the equation of the line.
Slope intercept form: y = mx + b (m = slope and b = y-intercept)
y = 1/2x
Lets find the exponential equation for the line.
y = ab²
1 = ab²
1/a = ab²/a
1/a = b²
√1/a = √b²
√1/a = b
<em>A graph of the coordinates will be below.</em>
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Best of Luck!
