The equation of the line is y = (5/2)x + 13/2
<h3>Why is the equation of a line?</h3>
Y = a, where an is the y-coordinate of the line's points, is the equation for lines that are horizontal or parallel to the X-axis. A straight line that is vertical or parallel to the Y-axis has the equation x = a, where an is the x-coordinate of each point along the line.
<h3>How do you solve an equation of a line?</h3>
Recognize the slope.
Decide on the point.
In the point-slope form, y y 1 = m (x x 1), substitute the values. y − y 1 = m (x − x 1) .
Slope-intercept form should be used to write the equation.
Rearrange the equation for a single y on one side to account for the gradient:
Step one is 5y = -2x - 3, followed by y = -(2/5)x - (3/5)
The x coefficient of the gradient is -(2/5), thus the perpendicular will be 5/2, which is its reciprocal in the negative.
Therefore, we need a line with a 5/2 gradient that goes across (-1,4).
It should start out as y = (5/2)x...
When we look at (-1,4), the y should be -(5/2), but because it is 4, we must add 13/2 to the equation to make it true.
y = (5/2)x + 13/2
This may be changed to -(5/2)x + y = 13/2 and then -5x + 2y = 13 if desired.
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