Question

# Determine the general equation of the straight line that passes through the point P $2;-3$ and is parallel to the straight line with the equation 5x – 2y 1 = 0:

210

likes
1049 views

## Answer to a math question Determine the general equation of the straight line that passes through the point P $2;-3$ and is parallel to the straight line with the equation 5x – 2y 1 = 0:

Maude
4.7
To find the equation of a line parallel to $5x - 2y + 1 = 0$ and passing through point $P$2, -3$$, we need to determine the slope of the given line first. The equation $5x - 2y + 1 = 0$ can be rewritten in the slope-intercept form $y = mx + c$ by rearranging it: $5x - 2y + 1 = 0$ $2y = 5x + 1$ $y = \frac{5}{2}x + \frac{1}{2}$ From this form, we see that the slope of the line is $m = \frac{5}{2}$. A line parallel to this line will have the same slope. So, the slope $$m$$ of the line we're looking for is also $m = \frac{5}{2}$. Now that we have the slope and the point $P$2, -3$$, we can use the point-slope form of the equation of a line: $y - y_1 = m$x - x_1$$ Substitute $4$x_1 = 2$, $y_1 = -3$, and $m = \frac{5}{2}$$\$: $y - $-3$ = \frac{5}{2}$x - 2$$ $y + 3 = \frac{5}{2}x - 5$ $y = \frac{5}{2}x - 5 - 3$ $y = \frac{5}{2}x - 8$ Therefore, the general equation of the straight line passing through point $P$2, -3$$ and parallel to the line $5x - 2y + 1 = 0$ is $y = \frac{5}{2}x - 8$.
Frequently asked questions $FAQs$
Find the value of x such that the reciprocal function f$x$ = 1/x equals its own inverse.